John Baez started counting.

"$0$, $1$, $2$, $3$, ... ".

After a long while, he noticed that the stars had all gone out, and even the black holes were dissipating. He went on counting.

"46893857378768993700351045289846783784571, 46893857378768993700351045289846783784572, 46893857378768993700351045289846783784573, ... ".

After much more time, he noticed he had run out of natural numbers and that the universe was over and done with. Interesting, he thought. I never thought I would live this long. He went on counting.

"$\omega$, $\omega +1$, $\omega +2$, $\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega +\omega$.

"$\omega 2$, $\omega 2+1$, $\omega 2+2$, $\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 2+\omega$.

"$\omega 3$, $\omega 3+1$, $\omega 3+2$, $\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 2$.

"$\omega 2$, $\omega 2+1$, $\omega 2+2$, $\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 2+\omega$.

"$\omega 2+\omega$, $\omega 2+\omega +1$, $\omega 2+\omega +2$, $\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 2+\omega +\omega$.

"$\omega 2+\omega 2$, $\omega 2+\omega 2+1$, $\omega 2+\omega 2+2$, $\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 2+\omega 2+\omega$.

"$\omega 2+\omega 3$, $\omega 2+\omega 3+1$, $\omega 2+\omega 3+2$, $\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 2+\omega 2$.

"$\omega 22$, $\omega 22+1$, $\omega 22+2$, $\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 22+\omega$.

"$\omega 22+\omega$, $\omega 22+\omega +1$, $\omega 22+\omega +2$, $\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 22+\omega +\omega$.

"$\omega 22+\omega 2$, $\omega 22+\omega 2+1$, $\omega 22+\omega 2+2$, $\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 22+\omega 2+\omega$.

"$\omega 22+\omega 3$, $\omega 22+\omega 3+1$, $\omega 22+\omega 3+2$, $\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 22+\omega 2$.

"$\omega 23$, $\omega 23+1$, $\omega 23+2$, $\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 23+\omega$.

"$\omega 23+\omega$, $\omega 23+\omega +1$, $\omega 23+\omega +2$, $\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 23+\omega +\omega$.

"$\omega 23+\omega 2$, $\omega 23+\omega 2+1$, $\omega 23+\omega 2+2$, $\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 23+\omega 2+\omega$.

"$\omega 23+\omega 3$, $\omega 23+\omega 3+1$, $\omega 23+\omega 3+2$, $\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3$.

"$\omega 3$, $\omega 3+1$, $\omega 3+2$, $\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega$.

"$\omega 3+\omega$, $\omega 3+\omega +1$, $\omega 3+\omega +2$, $\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega +\omega$.

"$\omega 3+\omega 2$, $\omega 3+\omega 2+1$, $\omega 3+\omega 2+2$, $\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 2+\omega$.

"$\omega 3+\omega 3$, $\omega 3+\omega 3+1$, $\omega 3+\omega 3+2$, $\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 2$.

"$\omega 3+\omega 2$, $\omega 3+\omega 2+1$, $\omega 3+\omega 2+2$, $\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 2+\omega$.

"$\omega 3+\omega 2+\omega$, $\omega 3+\omega 2+\omega +1$, $\omega 3+\omega 2+\omega +2$, $\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 2+\omega +\omega$.

"$\omega 3+\omega 2+\omega 2$, $\omega 3+\omega 2+\omega 2+1$, $\omega 3+\omega 2+\omega 2+2$, $\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 2+\omega 2+\omega$.

"$\omega 3+\omega 2+\omega 3$, $\omega 3+\omega 2+\omega 3+1$, $\omega 3+\omega 2+\omega 3+2$, $\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 2+\omega 2$.

"$\omega 3+\omega 22$, $\omega 3+\omega 22+1$, $\omega 3+\omega 22+2$, $\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 22+\omega$.

"$\omega 3+\omega 22+\omega$, $\omega 3+\omega 22+\omega +1$, $\omega 3+\omega 22+\omega +2$, $\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 22+\omega +\omega$.

"$\omega 3+\omega 22+\omega 2$, $\omega 3+\omega 22+\omega 2+1$, $\omega 3+\omega 22+\omega 2+2$, $\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 22+\omega 2+\omega$.

"$\omega 3+\omega 22+\omega 3$, $\omega 3+\omega 22+\omega 3+1$, $\omega 3+\omega 22+\omega 3+2$, $\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 22+\omega 2$.

"$\omega 3+\omega 23$, $\omega 3+\omega 23+1$, $\omega 3+\omega 23+2$, $\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 23+\omega$.

"$\omega 3+\omega 23+\omega$, $\omega 3+\omega 23+\omega +1$, $\omega 3+\omega 23+\omega +2$, $\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 23+\omega +\omega$.

"$\omega 3+\omega 23+\omega 2$, $\omega 3+\omega 23+\omega 2+1$, $\omega 3+\omega 23+\omega 2+2$, $\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 23+\omega 2+\omega$.

"$\omega 3+\omega 23+\omega 3$, $\omega 3+\omega 23+\omega 3+1$, $\omega 3+\omega 23+\omega 3+2$, $\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 3+\omega 3$.

"$\omega 32$, $\omega 32+1$, $\omega 32+2$, $\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega$.

"$\omega 32+\omega$, $\omega 32+\omega +1$, $\omega 32+\omega +2$, $\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega +\omega$.

"$\omega 32+\omega 2$, $\omega 32+\omega 2+1$, $\omega 32+\omega 2+2$, $\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 2+\omega$.

"$\omega 32+\omega 3$, $\omega 32+\omega 3+1$, $\omega 32+\omega 3+2$, $\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 2$.

"$\omega 32+\omega 2$, $\omega 32+\omega 2+1$, $\omega 32+\omega 2+2$, $\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 2+\omega$.

"$\omega 32+\omega 2+\omega$, $\omega 32+\omega 2+\omega +1$, $\omega 32+\omega 2+\omega +2$, $\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 2+\omega +\omega$.

"$\omega 32+\omega 2+\omega 2$, $\omega 32+\omega 2+\omega 2+1$, $\omega 32+\omega 2+\omega 2+2$, $\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 2+\omega 2+\omega$.

"$\omega 32+\omega 2+\omega 3$, $\omega 32+\omega 2+\omega 3+1$, $\omega 32+\omega 2+\omega 3+2$, $\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 2+\omega 2$.

"$\omega 32+\omega 22$, $\omega 32+\omega 22+1$, $\omega 32+\omega 22+2$, $\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 22+\omega$.

"$\omega 32+\omega 22+\omega$, $\omega 32+\omega 22+\omega +1$, $\omega 32+\omega 22+\omega +2$, $\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 22+\omega +\omega$.

"$\omega 32+\omega 22+\omega 2$, $\omega 32+\omega 22+\omega 2+1$, $\omega 32+\omega 22+\omega 2+2$, $\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 22+\omega 2+\omega$.

"$\omega 32+\omega 22+\omega 3$, $\omega 32+\omega 22+\omega 3+1$, $\omega 32+\omega 22+\omega 3+2$, $\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 22+\omega 2$.

"$\omega 32+\omega 23$, $\omega 32+\omega 23+1$, $\omega 32+\omega 23+2$, $\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 23+\omega$.

"$\omega 32+\omega 23+\omega$, $\omega 32+\omega 23+\omega +1$, $\omega 32+\omega 23+\omega +2$, $\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 23+\omega +\omega$.

"$\omega 32+\omega 23+\omega 2$, $\omega 32+\omega 23+\omega 2+1$, $\omega 32+\omega 23+\omega 2+2$, $\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 23+\omega 2+\omega$.

"$\omega 32+\omega 23+\omega 3$, $\omega 32+\omega 23+\omega 3+1$, $\omega 32+\omega 23+\omega 3+2$, $\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 32+\omega 3$.

"$\omega 33$, $\omega 33+1$, $\omega 33+2$, $\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega$.

"$\omega 33+\omega$, $\omega 33+\omega +1$, $\omega 33+\omega +2$, $\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega +\omega$.

"$\omega 33+\omega 2$, $\omega 33+\omega 2+1$, $\omega 33+\omega 2+2$, $\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 2+\omega$.

"$\omega 33+\omega 3$, $\omega 33+\omega 3+1$, $\omega 33+\omega 3+2$, $\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 2$.

"$\omega 33+\omega 2$, $\omega 33+\omega 2+1$, $\omega 33+\omega 2+2$, $\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 2+\omega$.

"$\omega 33+\omega 2+\omega$, $\omega 33+\omega 2+\omega +1$, $\omega 33+\omega 2+\omega +2$, $\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 2+\omega +\omega$.

"$\omega 33+\omega 2+\omega 2$, $\omega 33+\omega 2+\omega 2+1$, $\omega 33+\omega 2+\omega 2+2$, $\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 2+\omega 2+\omega$.

"$\omega 33+\omega 2+\omega 3$, $\omega 33+\omega 2+\omega 3+1$, $\omega 33+\omega 2+\omega 3+2$, $\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 2+\omega 2$.

"$\omega 33+\omega 22$, $\omega 33+\omega 22+1$, $\omega 33+\omega 22+2$, $\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 22+\omega$.

"$\omega 33+\omega 22+\omega$, $\omega 33+\omega 22+\omega +1$, $\omega 33+\omega 22+\omega +2$, $\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 22+\omega +\omega$.

"$\omega 33+\omega 22+\omega 2$, $\omega 33+\omega 22+\omega 2+1$, $\omega 33+\omega 22+\omega 2+2$, $\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 22+\omega 2+\omega$.

"$\omega 33+\omega 22+\omega 3$, $\omega 33+\omega 22+\omega 3+1$, $\omega 33+\omega 22+\omega 3+2$, $\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 22+\omega 2$.

"$\omega 33+\omega 23$, $\omega 33+\omega 23+1$, $\omega 33+\omega 23+2$, $\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 23+\omega$.

"$\omega 33+\omega 23+\omega$, $\omega 33+\omega 23+\omega +1$, $\omega 33+\omega 23+\omega +2$, $\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 23+\omega +\omega$.

"$\omega 33+\omega 23+\omega 2$, $\omega 33+\omega 23+\omega 2+1$, $\omega 33+\omega 23+\omega 2+2$, $\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 23+\omega 2+\omega$.

"$\omega 33+\omega 23+\omega 3$, $\omega 33+\omega 23+\omega 3+1$, $\omega 33+\omega 23+\omega 3+2$, $\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega 33+\omega 3$.

...

Eventually he ran out of integers for the powers of omega. Never mind, he had all the ordinals available to count powers of omega.

"$\omega \omega$, $\omega \omega +1$, $\omega \omega +2$, $\omega \omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega$.

"$\omega \omega +\omega$, $\omega \omega +\omega +1$, $\omega \omega +\omega +2$, $\omega \omega +\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega +\omega$.

"$\omega \omega +\omega 2$, $\omega \omega +\omega 2+1$, $\omega \omega +\omega 2+2$, $\omega \omega +\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 2+\omega$.

"$\omega \omega +\omega 3$, $\omega \omega +\omega 3+1$, $\omega \omega +\omega 3+2$, $\omega \omega +\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 2$.

"$\omega \omega +\omega 2$, $\omega \omega +\omega 2+1$, $\omega \omega +\omega 2+2$, $\omega \omega +\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 2+\omega$.

"$\omega \omega +\omega 2+\omega$, $\omega \omega +\omega 2+\omega +1$, $\omega \omega +\omega 2+\omega +2$, $\omega \omega +\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 2+\omega +\omega$.

"$\omega \omega +\omega 2+\omega 2$, $\omega \omega +\omega 2+\omega 2+1$, $\omega \omega +\omega 2+\omega 2+2$, $\omega \omega +\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 2+\omega 2+\omega$.

"$\omega \omega +\omega 2+\omega 3$, $\omega \omega +\omega 2+\omega 3+1$, $\omega \omega +\omega 2+\omega 3+2$, $\omega \omega +\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 2+\omega 2$.

"$\omega \omega +\omega 22$, $\omega \omega +\omega 22+1$, $\omega \omega +\omega 22+2$, $\omega \omega +\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 22+\omega$.

"$\omega \omega +\omega 22+\omega$, $\omega \omega +\omega 22+\omega +1$, $\omega \omega +\omega 22+\omega +2$, $\omega \omega +\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 22+\omega +\omega$.

"$\omega \omega +\omega 22+\omega 2$, $\omega \omega +\omega 22+\omega 2+1$, $\omega \omega +\omega 22+\omega 2+2$, $\omega \omega +\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 22+\omega 2+\omega$.

"$\omega \omega +\omega 22+\omega 3$, $\omega \omega +\omega 22+\omega 3+1$, $\omega \omega +\omega 22+\omega 3+2$, $\omega \omega +\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 22+\omega 2$.

"$\omega \omega +\omega 23$, $\omega \omega +\omega 23+1$, $\omega \omega +\omega 23+2$, $\omega \omega +\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 23+\omega$.

"$\omega \omega +\omega 23+\omega$, $\omega \omega +\omega 23+\omega +1$, $\omega \omega +\omega 23+\omega +2$, $\omega \omega +\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 23+\omega +\omega$.

"$\omega \omega +\omega 23+\omega 2$, $\omega \omega +\omega 23+\omega 2+1$, $\omega \omega +\omega 23+\omega 2+2$, $\omega \omega +\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 23+\omega 2+\omega$.

"$\omega \omega +\omega 23+\omega 3$, $\omega \omega +\omega 23+\omega 3+1$, $\omega \omega +\omega 23+\omega 3+2$, $\omega \omega +\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3$.

"$\omega \omega +\omega 3$, $\omega \omega +\omega 3+1$, $\omega \omega +\omega 3+2$, $\omega \omega +\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega$.

"$\omega \omega +\omega 3+\omega$, $\omega \omega +\omega 3+\omega +1$, $\omega \omega +\omega 3+\omega +2$, $\omega \omega +\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega +\omega$.

"$\omega \omega +\omega 3+\omega 2$, $\omega \omega +\omega 3+\omega 2+1$, $\omega \omega +\omega 3+\omega 2+2$, $\omega \omega +\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 2+\omega$.

"$\omega \omega +\omega 3+\omega 3$, $\omega \omega +\omega 3+\omega 3+1$, $\omega \omega +\omega 3+\omega 3+2$, $\omega \omega +\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 2$.

"$\omega \omega +\omega 3+\omega 2$, $\omega \omega +\omega 3+\omega 2+1$, $\omega \omega +\omega 3+\omega 2+2$, $\omega \omega +\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 2+\omega$.

"$\omega \omega +\omega 3+\omega 2+\omega$, $\omega \omega +\omega 3+\omega 2+\omega +1$, $\omega \omega +\omega 3+\omega 2+\omega +2$, $\omega \omega +\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega +\omega 3+\omega 2+\omega 2$, $\omega \omega +\omega 3+\omega 2+\omega 2+1$, $\omega \omega +\omega 3+\omega 2+\omega 2+2$, $\omega \omega +\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega +\omega 3+\omega 2+\omega 3$, $\omega \omega +\omega 3+\omega 2+\omega 3+1$, $\omega \omega +\omega 3+\omega 2+\omega 3+2$, $\omega \omega +\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 2+\omega 2$.

"$\omega \omega +\omega 3+\omega 22$, $\omega \omega +\omega 3+\omega 22+1$, $\omega \omega +\omega 3+\omega 22+2$, $\omega \omega +\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 22+\omega$.

"$\omega \omega +\omega 3+\omega 22+\omega$, $\omega \omega +\omega 3+\omega 22+\omega +1$, $\omega \omega +\omega 3+\omega 22+\omega +2$, $\omega \omega +\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega +\omega 3+\omega 22+\omega 2$, $\omega \omega +\omega 3+\omega 22+\omega 2+1$, $\omega \omega +\omega 3+\omega 22+\omega 2+2$, $\omega \omega +\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega +\omega 3+\omega 22+\omega 3$, $\omega \omega +\omega 3+\omega 22+\omega 3+1$, $\omega \omega +\omega 3+\omega 22+\omega 3+2$, $\omega \omega +\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 22+\omega 2$.

"$\omega \omega +\omega 3+\omega 23$, $\omega \omega +\omega 3+\omega 23+1$, $\omega \omega +\omega 3+\omega 23+2$, $\omega \omega +\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 23+\omega$.

"$\omega \omega +\omega 3+\omega 23+\omega$, $\omega \omega +\omega 3+\omega 23+\omega +1$, $\omega \omega +\omega 3+\omega 23+\omega +2$, $\omega \omega +\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega +\omega 3+\omega 23+\omega 2$, $\omega \omega +\omega 3+\omega 23+\omega 2+1$, $\omega \omega +\omega 3+\omega 23+\omega 2+2$, $\omega \omega +\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega +\omega 3+\omega 23+\omega 3$, $\omega \omega +\omega 3+\omega 23+\omega 3+1$, $\omega \omega +\omega 3+\omega 23+\omega 3+2$, $\omega \omega +\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 3+\omega 3$.

"$\omega \omega +\omega 32$, $\omega \omega +\omega 32+1$, $\omega \omega +\omega 32+2$, $\omega \omega +\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega$.

"$\omega \omega +\omega 32+\omega$, $\omega \omega +\omega 32+\omega +1$, $\omega \omega +\omega 32+\omega +2$, $\omega \omega +\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega +\omega$.

"$\omega \omega +\omega 32+\omega 2$, $\omega \omega +\omega 32+\omega 2+1$, $\omega \omega +\omega 32+\omega 2+2$, $\omega \omega +\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 2+\omega$.

"$\omega \omega +\omega 32+\omega 3$, $\omega \omega +\omega 32+\omega 3+1$, $\omega \omega +\omega 32+\omega 3+2$, $\omega \omega +\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 2$.

"$\omega \omega +\omega 32+\omega 2$, $\omega \omega +\omega 32+\omega 2+1$, $\omega \omega +\omega 32+\omega 2+2$, $\omega \omega +\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 2+\omega$.

"$\omega \omega +\omega 32+\omega 2+\omega$, $\omega \omega +\omega 32+\omega 2+\omega +1$, $\omega \omega +\omega 32+\omega 2+\omega +2$, $\omega \omega +\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega +\omega 32+\omega 2+\omega 2$, $\omega \omega +\omega 32+\omega 2+\omega 2+1$, $\omega \omega +\omega 32+\omega 2+\omega 2+2$, $\omega \omega +\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega +\omega 32+\omega 2+\omega 3$, $\omega \omega +\omega 32+\omega 2+\omega 3+1$, $\omega \omega +\omega 32+\omega 2+\omega 3+2$, $\omega \omega +\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 2+\omega 2$.

"$\omega \omega +\omega 32+\omega 22$, $\omega \omega +\omega 32+\omega 22+1$, $\omega \omega +\omega 32+\omega 22+2$, $\omega \omega +\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 22+\omega$.

"$\omega \omega +\omega 32+\omega 22+\omega$, $\omega \omega +\omega 32+\omega 22+\omega +1$, $\omega \omega +\omega 32+\omega 22+\omega +2$, $\omega \omega +\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega +\omega 32+\omega 22+\omega 2$, $\omega \omega +\omega 32+\omega 22+\omega 2+1$, $\omega \omega +\omega 32+\omega 22+\omega 2+2$, $\omega \omega +\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega +\omega 32+\omega 22+\omega 3$, $\omega \omega +\omega 32+\omega 22+\omega 3+1$, $\omega \omega +\omega 32+\omega 22+\omega 3+2$, $\omega \omega +\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 22+\omega 2$.

"$\omega \omega +\omega 32+\omega 23$, $\omega \omega +\omega 32+\omega 23+1$, $\omega \omega +\omega 32+\omega 23+2$, $\omega \omega +\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 23+\omega$.

"$\omega \omega +\omega 32+\omega 23+\omega$, $\omega \omega +\omega 32+\omega 23+\omega +1$, $\omega \omega +\omega 32+\omega 23+\omega +2$, $\omega \omega +\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega +\omega 32+\omega 23+\omega 2$, $\omega \omega +\omega 32+\omega 23+\omega 2+1$, $\omega \omega +\omega 32+\omega 23+\omega 2+2$, $\omega \omega +\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega +\omega 32+\omega 23+\omega 3$, $\omega \omega +\omega 32+\omega 23+\omega 3+1$, $\omega \omega +\omega 32+\omega 23+\omega 3+2$, $\omega \omega +\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 32+\omega 3$.

"$\omega \omega +\omega 33$, $\omega \omega +\omega 33+1$, $\omega \omega +\omega 33+2$, $\omega \omega +\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega$.

"$\omega \omega +\omega 33+\omega$, $\omega \omega +\omega 33+\omega +1$, $\omega \omega +\omega 33+\omega +2$, $\omega \omega +\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega +\omega$.

"$\omega \omega +\omega 33+\omega 2$, $\omega \omega +\omega 33+\omega 2+1$, $\omega \omega +\omega 33+\omega 2+2$, $\omega \omega +\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 2+\omega$.

"$\omega \omega +\omega 33+\omega 3$, $\omega \omega +\omega 33+\omega 3+1$, $\omega \omega +\omega 33+\omega 3+2$, $\omega \omega +\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 2$.

"$\omega \omega +\omega 33+\omega 2$, $\omega \omega +\omega 33+\omega 2+1$, $\omega \omega +\omega 33+\omega 2+2$, $\omega \omega +\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 2+\omega$.

"$\omega \omega +\omega 33+\omega 2+\omega$, $\omega \omega +\omega 33+\omega 2+\omega +1$, $\omega \omega +\omega 33+\omega 2+\omega +2$, $\omega \omega +\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega +\omega 33+\omega 2+\omega 2$, $\omega \omega +\omega 33+\omega 2+\omega 2+1$, $\omega \omega +\omega 33+\omega 2+\omega 2+2$, $\omega \omega +\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega +\omega 33+\omega 2+\omega 3$, $\omega \omega +\omega 33+\omega 2+\omega 3+1$, $\omega \omega +\omega 33+\omega 2+\omega 3+2$, $\omega \omega +\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 2+\omega 2$.

"$\omega \omega +\omega 33+\omega 22$, $\omega \omega +\omega 33+\omega 22+1$, $\omega \omega +\omega 33+\omega 22+2$, $\omega \omega +\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 22+\omega$.

"$\omega \omega +\omega 33+\omega 22+\omega$, $\omega \omega +\omega 33+\omega 22+\omega +1$, $\omega \omega +\omega 33+\omega 22+\omega +2$, $\omega \omega +\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega +\omega 33+\omega 22+\omega 2$, $\omega \omega +\omega 33+\omega 22+\omega 2+1$, $\omega \omega +\omega 33+\omega 22+\omega 2+2$, $\omega \omega +\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega +\omega 33+\omega 22+\omega 3$, $\omega \omega +\omega 33+\omega 22+\omega 3+1$, $\omega \omega +\omega 33+\omega 22+\omega 3+2$, $\omega \omega +\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 22+\omega 2$.

"$\omega \omega +\omega 33+\omega 23$, $\omega \omega +\omega 33+\omega 23+1$, $\omega \omega +\omega 33+\omega 23+2$, $\omega \omega +\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 23+\omega$.

"$\omega \omega +\omega 33+\omega 23+\omega$, $\omega \omega +\omega 33+\omega 23+\omega +1$, $\omega \omega +\omega 33+\omega 23+\omega +2$, $\omega \omega +\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega +\omega 33+\omega 23+\omega 2$, $\omega \omega +\omega 33+\omega 23+\omega 2+1$, $\omega \omega +\omega 33+\omega 23+\omega 2+2$, $\omega \omega +\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega +\omega 33+\omega 23+\omega 3$, $\omega \omega +\omega 33+\omega 23+\omega 3+1$, $\omega \omega +\omega 33+\omega 23+\omega 3+2$, $\omega \omega +\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +\omega 33+\omega 3$.

"$\omega \omega 2$, $\omega \omega 2+1$, $\omega \omega 2+2$, $\omega \omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega$.

"$\omega \omega 2+\omega$, $\omega \omega 2+\omega +1$, $\omega \omega 2+\omega +2$, $\omega \omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega +\omega$.

"$\omega \omega 2+\omega 2$, $\omega \omega 2+\omega 2+1$, $\omega \omega 2+\omega 2+2$, $\omega \omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 2+\omega$.

"$\omega \omega 2+\omega 3$, $\omega \omega 2+\omega 3+1$, $\omega \omega 2+\omega 3+2$, $\omega \omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 2$.

"$\omega \omega 2+\omega 2$, $\omega \omega 2+\omega 2+1$, $\omega \omega 2+\omega 2+2$, $\omega \omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 2+\omega$.

"$\omega \omega 2+\omega 2+\omega$, $\omega \omega 2+\omega 2+\omega +1$, $\omega \omega 2+\omega 2+\omega +2$, $\omega \omega 2+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 2+\omega +\omega$.

"$\omega \omega 2+\omega 2+\omega 2$, $\omega \omega 2+\omega 2+\omega 2+1$, $\omega \omega 2+\omega 2+\omega 2+2$, $\omega \omega 2+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 2+\omega 2+\omega$.

"$\omega \omega 2+\omega 2+\omega 3$, $\omega \omega 2+\omega 2+\omega 3+1$, $\omega \omega 2+\omega 2+\omega 3+2$, $\omega \omega 2+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 2+\omega 2$.

"$\omega \omega 2+\omega 22$, $\omega \omega 2+\omega 22+1$, $\omega \omega 2+\omega 22+2$, $\omega \omega 2+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 22+\omega$.

"$\omega \omega 2+\omega 22+\omega$, $\omega \omega 2+\omega 22+\omega +1$, $\omega \omega 2+\omega 22+\omega +2$, $\omega \omega 2+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 22+\omega +\omega$.

"$\omega \omega 2+\omega 22+\omega 2$, $\omega \omega 2+\omega 22+\omega 2+1$, $\omega \omega 2+\omega 22+\omega 2+2$, $\omega \omega 2+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 22+\omega 2+\omega$.

"$\omega \omega 2+\omega 22+\omega 3$, $\omega \omega 2+\omega 22+\omega 3+1$, $\omega \omega 2+\omega 22+\omega 3+2$, $\omega \omega 2+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 22+\omega 2$.

"$\omega \omega 2+\omega 23$, $\omega \omega 2+\omega 23+1$, $\omega \omega 2+\omega 23+2$, $\omega \omega 2+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 23+\omega$.

"$\omega \omega 2+\omega 23+\omega$, $\omega \omega 2+\omega 23+\omega +1$, $\omega \omega 2+\omega 23+\omega +2$, $\omega \omega 2+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 23+\omega +\omega$.

"$\omega \omega 2+\omega 23+\omega 2$, $\omega \omega 2+\omega 23+\omega 2+1$, $\omega \omega 2+\omega 23+\omega 2+2$, $\omega \omega 2+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 23+\omega 2+\omega$.

"$\omega \omega 2+\omega 23+\omega 3$, $\omega \omega 2+\omega 23+\omega 3+1$, $\omega \omega 2+\omega 23+\omega 3+2$, $\omega \omega 2+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3$.

"$\omega \omega 2+\omega 3$, $\omega \omega 2+\omega 3+1$, $\omega \omega 2+\omega 3+2$, $\omega \omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega$.

"$\omega \omega 2+\omega 3+\omega$, $\omega \omega 2+\omega 3+\omega +1$, $\omega \omega 2+\omega 3+\omega +2$, $\omega \omega 2+\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega +\omega$.

"$\omega \omega 2+\omega 3+\omega 2$, $\omega \omega 2+\omega 3+\omega 2+1$, $\omega \omega 2+\omega 3+\omega 2+2$, $\omega \omega 2+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 2+\omega$.

"$\omega \omega 2+\omega 3+\omega 3$, $\omega \omega 2+\omega 3+\omega 3+1$, $\omega \omega 2+\omega 3+\omega 3+2$, $\omega \omega 2+\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 2$.

"$\omega \omega 2+\omega 3+\omega 2$, $\omega \omega 2+\omega 3+\omega 2+1$, $\omega \omega 2+\omega 3+\omega 2+2$, $\omega \omega 2+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 2+\omega$.

"$\omega \omega 2+\omega 3+\omega 2+\omega$, $\omega \omega 2+\omega 3+\omega 2+\omega +1$, $\omega \omega 2+\omega 3+\omega 2+\omega +2$, $\omega \omega 2+\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega 2+\omega 3+\omega 2+\omega 2$, $\omega \omega 2+\omega 3+\omega 2+\omega 2+1$, $\omega \omega 2+\omega 3+\omega 2+\omega 2+2$, $\omega \omega 2+\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega 2+\omega 3+\omega 2+\omega 3$, $\omega \omega 2+\omega 3+\omega 2+\omega 3+1$, $\omega \omega 2+\omega 3+\omega 2+\omega 3+2$, $\omega \omega 2+\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 2+\omega 2$.

"$\omega \omega 2+\omega 3+\omega 22$, $\omega \omega 2+\omega 3+\omega 22+1$, $\omega \omega 2+\omega 3+\omega 22+2$, $\omega \omega 2+\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 22+\omega$.

"$\omega \omega 2+\omega 3+\omega 22+\omega$, $\omega \omega 2+\omega 3+\omega 22+\omega +1$, $\omega \omega 2+\omega 3+\omega 22+\omega +2$, $\omega \omega 2+\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega 2+\omega 3+\omega 22+\omega 2$, $\omega \omega 2+\omega 3+\omega 22+\omega 2+1$, $\omega \omega 2+\omega 3+\omega 22+\omega 2+2$, $\omega \omega 2+\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega 2+\omega 3+\omega 22+\omega 3$, $\omega \omega 2+\omega 3+\omega 22+\omega 3+1$, $\omega \omega 2+\omega 3+\omega 22+\omega 3+2$, $\omega \omega 2+\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 22+\omega 2$.

"$\omega \omega 2+\omega 3+\omega 23$, $\omega \omega 2+\omega 3+\omega 23+1$, $\omega \omega 2+\omega 3+\omega 23+2$, $\omega \omega 2+\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 23+\omega$.

"$\omega \omega 2+\omega 3+\omega 23+\omega$, $\omega \omega 2+\omega 3+\omega 23+\omega +1$, $\omega \omega 2+\omega 3+\omega 23+\omega +2$, $\omega \omega 2+\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega 2+\omega 3+\omega 23+\omega 2$, $\omega \omega 2+\omega 3+\omega 23+\omega 2+1$, $\omega \omega 2+\omega 3+\omega 23+\omega 2+2$, $\omega \omega 2+\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega 2+\omega 3+\omega 23+\omega 3$, $\omega \omega 2+\omega 3+\omega 23+\omega 3+1$, $\omega \omega 2+\omega 3+\omega 23+\omega 3+2$, $\omega \omega 2+\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 3+\omega 3$.

"$\omega \omega 2+\omega 32$, $\omega \omega 2+\omega 32+1$, $\omega \omega 2+\omega 32+2$, $\omega \omega 2+\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega$.

"$\omega \omega 2+\omega 32+\omega$, $\omega \omega 2+\omega 32+\omega +1$, $\omega \omega 2+\omega 32+\omega +2$, $\omega \omega 2+\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega +\omega$.

"$\omega \omega 2+\omega 32+\omega 2$, $\omega \omega 2+\omega 32+\omega 2+1$, $\omega \omega 2+\omega 32+\omega 2+2$, $\omega \omega 2+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 2+\omega$.

"$\omega \omega 2+\omega 32+\omega 3$, $\omega \omega 2+\omega 32+\omega 3+1$, $\omega \omega 2+\omega 32+\omega 3+2$, $\omega \omega 2+\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 2$.

"$\omega \omega 2+\omega 32+\omega 2$, $\omega \omega 2+\omega 32+\omega 2+1$, $\omega \omega 2+\omega 32+\omega 2+2$, $\omega \omega 2+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 2+\omega$.

"$\omega \omega 2+\omega 32+\omega 2+\omega$, $\omega \omega 2+\omega 32+\omega 2+\omega +1$, $\omega \omega 2+\omega 32+\omega 2+\omega +2$, $\omega \omega 2+\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega 2+\omega 32+\omega 2+\omega 2$, $\omega \omega 2+\omega 32+\omega 2+\omega 2+1$, $\omega \omega 2+\omega 32+\omega 2+\omega 2+2$, $\omega \omega 2+\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega 2+\omega 32+\omega 2+\omega 3$, $\omega \omega 2+\omega 32+\omega 2+\omega 3+1$, $\omega \omega 2+\omega 32+\omega 2+\omega 3+2$, $\omega \omega 2+\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 2+\omega 2$.

"$\omega \omega 2+\omega 32+\omega 22$, $\omega \omega 2+\omega 32+\omega 22+1$, $\omega \omega 2+\omega 32+\omega 22+2$, $\omega \omega 2+\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 22+\omega$.

"$\omega \omega 2+\omega 32+\omega 22+\omega$, $\omega \omega 2+\omega 32+\omega 22+\omega +1$, $\omega \omega 2+\omega 32+\omega 22+\omega +2$, $\omega \omega 2+\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega 2+\omega 32+\omega 22+\omega 2$, $\omega \omega 2+\omega 32+\omega 22+\omega 2+1$, $\omega \omega 2+\omega 32+\omega 22+\omega 2+2$, $\omega \omega 2+\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega 2+\omega 32+\omega 22+\omega 3$, $\omega \omega 2+\omega 32+\omega 22+\omega 3+1$, $\omega \omega 2+\omega 32+\omega 22+\omega 3+2$, $\omega \omega 2+\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 22+\omega 2$.

"$\omega \omega 2+\omega 32+\omega 23$, $\omega \omega 2+\omega 32+\omega 23+1$, $\omega \omega 2+\omega 32+\omega 23+2$, $\omega \omega 2+\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 23+\omega$.

"$\omega \omega 2+\omega 32+\omega 23+\omega$, $\omega \omega 2+\omega 32+\omega 23+\omega +1$, $\omega \omega 2+\omega 32+\omega 23+\omega +2$, $\omega \omega 2+\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega 2+\omega 32+\omega 23+\omega 2$, $\omega \omega 2+\omega 32+\omega 23+\omega 2+1$, $\omega \omega 2+\omega 32+\omega 23+\omega 2+2$, $\omega \omega 2+\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega 2+\omega 32+\omega 23+\omega 3$, $\omega \omega 2+\omega 32+\omega 23+\omega 3+1$, $\omega \omega 2+\omega 32+\omega 23+\omega 3+2$, $\omega \omega 2+\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 32+\omega 3$.

"$\omega \omega 2+\omega 33$, $\omega \omega 2+\omega 33+1$, $\omega \omega 2+\omega 33+2$, $\omega \omega 2+\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega$.

"$\omega \omega 2+\omega 33+\omega$, $\omega \omega 2+\omega 33+\omega +1$, $\omega \omega 2+\omega 33+\omega +2$, $\omega \omega 2+\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega +\omega$.

"$\omega \omega 2+\omega 33+\omega 2$, $\omega \omega 2+\omega 33+\omega 2+1$, $\omega \omega 2+\omega 33+\omega 2+2$, $\omega \omega 2+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 2+\omega$.

"$\omega \omega 2+\omega 33+\omega 3$, $\omega \omega 2+\omega 33+\omega 3+1$, $\omega \omega 2+\omega 33+\omega 3+2$, $\omega \omega 2+\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 2$.

"$\omega \omega 2+\omega 33+\omega 2$, $\omega \omega 2+\omega 33+\omega 2+1$, $\omega \omega 2+\omega 33+\omega 2+2$, $\omega \omega 2+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 2+\omega$.

"$\omega \omega 2+\omega 33+\omega 2+\omega$, $\omega \omega 2+\omega 33+\omega 2+\omega +1$, $\omega \omega 2+\omega 33+\omega 2+\omega +2$, $\omega \omega 2+\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega 2+\omega 33+\omega 2+\omega 2$, $\omega \omega 2+\omega 33+\omega 2+\omega 2+1$, $\omega \omega 2+\omega 33+\omega 2+\omega 2+2$, $\omega \omega 2+\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega 2+\omega 33+\omega 2+\omega 3$, $\omega \omega 2+\omega 33+\omega 2+\omega 3+1$, $\omega \omega 2+\omega 33+\omega 2+\omega 3+2$, $\omega \omega 2+\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 2+\omega 2$.

"$\omega \omega 2+\omega 33+\omega 22$, $\omega \omega 2+\omega 33+\omega 22+1$, $\omega \omega 2+\omega 33+\omega 22+2$, $\omega \omega 2+\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 22+\omega$.

"$\omega \omega 2+\omega 33+\omega 22+\omega$, $\omega \omega 2+\omega 33+\omega 22+\omega +1$, $\omega \omega 2+\omega 33+\omega 22+\omega +2$, $\omega \omega 2+\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega 2+\omega 33+\omega 22+\omega 2$, $\omega \omega 2+\omega 33+\omega 22+\omega 2+1$, $\omega \omega 2+\omega 33+\omega 22+\omega 2+2$, $\omega \omega 2+\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega 2+\omega 33+\omega 22+\omega 3$, $\omega \omega 2+\omega 33+\omega 22+\omega 3+1$, $\omega \omega 2+\omega 33+\omega 22+\omega 3+2$, $\omega \omega 2+\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 22+\omega 2$.

"$\omega \omega 2+\omega 33+\omega 23$, $\omega \omega 2+\omega 33+\omega 23+1$, $\omega \omega 2+\omega 33+\omega 23+2$, $\omega \omega 2+\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 23+\omega$.

"$\omega \omega 2+\omega 33+\omega 23+\omega$, $\omega \omega 2+\omega 33+\omega 23+\omega +1$, $\omega \omega 2+\omega 33+\omega 23+\omega +2$, $\omega \omega 2+\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega 2+\omega 33+\omega 23+\omega 2$, $\omega \omega 2+\omega 33+\omega 23+\omega 2+1$, $\omega \omega 2+\omega 33+\omega 23+\omega 2+2$, $\omega \omega 2+\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega 2+\omega 33+\omega 23+\omega 3$, $\omega \omega 2+\omega 33+\omega 23+\omega 3+1$, $\omega \omega 2+\omega 33+\omega 23+\omega 3+2$, $\omega \omega 2+\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 2+\omega 33+\omega 3$.

"$\omega \omega 3$, $\omega \omega 3+1$, $\omega \omega 3+2$, $\omega \omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega$.

"$\omega \omega 3+\omega$, $\omega \omega 3+\omega +1$, $\omega \omega 3+\omega +2$, $\omega \omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega +\omega$.

"$\omega \omega 3+\omega 2$, $\omega \omega 3+\omega 2+1$, $\omega \omega 3+\omega 2+2$, $\omega \omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 2+\omega$.

"$\omega \omega 3+\omega 3$, $\omega \omega 3+\omega 3+1$, $\omega \omega 3+\omega 3+2$, $\omega \omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 2$.

"$\omega \omega 3+\omega 2$, $\omega \omega 3+\omega 2+1$, $\omega \omega 3+\omega 2+2$, $\omega \omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 2+\omega$.

"$\omega \omega 3+\omega 2+\omega$, $\omega \omega 3+\omega 2+\omega +1$, $\omega \omega 3+\omega 2+\omega +2$, $\omega \omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 2+\omega +\omega$.

"$\omega \omega 3+\omega 2+\omega 2$, $\omega \omega 3+\omega 2+\omega 2+1$, $\omega \omega 3+\omega 2+\omega 2+2$, $\omega \omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega 3+\omega 2+\omega 3$, $\omega \omega 3+\omega 2+\omega 3+1$, $\omega \omega 3+\omega 2+\omega 3+2$, $\omega \omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 2+\omega 2$.

"$\omega \omega 3+\omega 22$, $\omega \omega 3+\omega 22+1$, $\omega \omega 3+\omega 22+2$, $\omega \omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 22+\omega$.

"$\omega \omega 3+\omega 22+\omega$, $\omega \omega 3+\omega 22+\omega +1$, $\omega \omega 3+\omega 22+\omega +2$, $\omega \omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 22+\omega +\omega$.

"$\omega \omega 3+\omega 22+\omega 2$, $\omega \omega 3+\omega 22+\omega 2+1$, $\omega \omega 3+\omega 22+\omega 2+2$, $\omega \omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega 3+\omega 22+\omega 3$, $\omega \omega 3+\omega 22+\omega 3+1$, $\omega \omega 3+\omega 22+\omega 3+2$, $\omega \omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 22+\omega 2$.

"$\omega \omega 3+\omega 23$, $\omega \omega 3+\omega 23+1$, $\omega \omega 3+\omega 23+2$, $\omega \omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 23+\omega$.

"$\omega \omega 3+\omega 23+\omega$, $\omega \omega 3+\omega 23+\omega +1$, $\omega \omega 3+\omega 23+\omega +2$, $\omega \omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 23+\omega +\omega$.

"$\omega \omega 3+\omega 23+\omega 2$, $\omega \omega 3+\omega 23+\omega 2+1$, $\omega \omega 3+\omega 23+\omega 2+2$, $\omega \omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega 3+\omega 23+\omega 3$, $\omega \omega 3+\omega 23+\omega 3+1$, $\omega \omega 3+\omega 23+\omega 3+2$, $\omega \omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3$.

"$\omega \omega 3+\omega 3$, $\omega \omega 3+\omega 3+1$, $\omega \omega 3+\omega 3+2$, $\omega \omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega$.

"$\omega \omega 3+\omega 3+\omega$, $\omega \omega 3+\omega 3+\omega +1$, $\omega \omega 3+\omega 3+\omega +2$, $\omega \omega 3+\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega +\omega$.

"$\omega \omega 3+\omega 3+\omega 2$, $\omega \omega 3+\omega 3+\omega 2+1$, $\omega \omega 3+\omega 3+\omega 2+2$, $\omega \omega 3+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 2+\omega$.

"$\omega \omega 3+\omega 3+\omega 3$, $\omega \omega 3+\omega 3+\omega 3+1$, $\omega \omega 3+\omega 3+\omega 3+2$, $\omega \omega 3+\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 2$.

"$\omega \omega 3+\omega 3+\omega 2$, $\omega \omega 3+\omega 3+\omega 2+1$, $\omega \omega 3+\omega 3+\omega 2+2$, $\omega \omega 3+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 2+\omega$.

"$\omega \omega 3+\omega 3+\omega 2+\omega$, $\omega \omega 3+\omega 3+\omega 2+\omega +1$, $\omega \omega 3+\omega 3+\omega 2+\omega +2$, $\omega \omega 3+\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega 3+\omega 3+\omega 2+\omega 2$, $\omega \omega 3+\omega 3+\omega 2+\omega 2+1$, $\omega \omega 3+\omega 3+\omega 2+\omega 2+2$, $\omega \omega 3+\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega 3+\omega 3+\omega 2+\omega 3$, $\omega \omega 3+\omega 3+\omega 2+\omega 3+1$, $\omega \omega 3+\omega 3+\omega 2+\omega 3+2$, $\omega \omega 3+\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 2+\omega 2$.

"$\omega \omega 3+\omega 3+\omega 22$, $\omega \omega 3+\omega 3+\omega 22+1$, $\omega \omega 3+\omega 3+\omega 22+2$, $\omega \omega 3+\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 22+\omega$.

"$\omega \omega 3+\omega 3+\omega 22+\omega$, $\omega \omega 3+\omega 3+\omega 22+\omega +1$, $\omega \omega 3+\omega 3+\omega 22+\omega +2$, $\omega \omega 3+\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega 3+\omega 3+\omega 22+\omega 2$, $\omega \omega 3+\omega 3+\omega 22+\omega 2+1$, $\omega \omega 3+\omega 3+\omega 22+\omega 2+2$, $\omega \omega 3+\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega 3+\omega 3+\omega 22+\omega 3$, $\omega \omega 3+\omega 3+\omega 22+\omega 3+1$, $\omega \omega 3+\omega 3+\omega 22+\omega 3+2$, $\omega \omega 3+\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 22+\omega 2$.

"$\omega \omega 3+\omega 3+\omega 23$, $\omega \omega 3+\omega 3+\omega 23+1$, $\omega \omega 3+\omega 3+\omega 23+2$, $\omega \omega 3+\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 23+\omega$.

"$\omega \omega 3+\omega 3+\omega 23+\omega$, $\omega \omega 3+\omega 3+\omega 23+\omega +1$, $\omega \omega 3+\omega 3+\omega 23+\omega +2$, $\omega \omega 3+\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega 3+\omega 3+\omega 23+\omega 2$, $\omega \omega 3+\omega 3+\omega 23+\omega 2+1$, $\omega \omega 3+\omega 3+\omega 23+\omega 2+2$, $\omega \omega 3+\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega 3+\omega 3+\omega 23+\omega 3$, $\omega \omega 3+\omega 3+\omega 23+\omega 3+1$, $\omega \omega 3+\omega 3+\omega 23+\omega 3+2$, $\omega \omega 3+\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 3+\omega 3$.

"$\omega \omega 3+\omega 32$, $\omega \omega 3+\omega 32+1$, $\omega \omega 3+\omega 32+2$, $\omega \omega 3+\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega$.

"$\omega \omega 3+\omega 32+\omega$, $\omega \omega 3+\omega 32+\omega +1$, $\omega \omega 3+\omega 32+\omega +2$, $\omega \omega 3+\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega +\omega$.

"$\omega \omega 3+\omega 32+\omega 2$, $\omega \omega 3+\omega 32+\omega 2+1$, $\omega \omega 3+\omega 32+\omega 2+2$, $\omega \omega 3+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 2+\omega$.

"$\omega \omega 3+\omega 32+\omega 3$, $\omega \omega 3+\omega 32+\omega 3+1$, $\omega \omega 3+\omega 32+\omega 3+2$, $\omega \omega 3+\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 2$.

"$\omega \omega 3+\omega 32+\omega 2$, $\omega \omega 3+\omega 32+\omega 2+1$, $\omega \omega 3+\omega 32+\omega 2+2$, $\omega \omega 3+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 2+\omega$.

"$\omega \omega 3+\omega 32+\omega 2+\omega$, $\omega \omega 3+\omega 32+\omega 2+\omega +1$, $\omega \omega 3+\omega 32+\omega 2+\omega +2$, $\omega \omega 3+\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega 3+\omega 32+\omega 2+\omega 2$, $\omega \omega 3+\omega 32+\omega 2+\omega 2+1$, $\omega \omega 3+\omega 32+\omega 2+\omega 2+2$, $\omega \omega 3+\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega 3+\omega 32+\omega 2+\omega 3$, $\omega \omega 3+\omega 32+\omega 2+\omega 3+1$, $\omega \omega 3+\omega 32+\omega 2+\omega 3+2$, $\omega \omega 3+\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 2+\omega 2$.

"$\omega \omega 3+\omega 32+\omega 22$, $\omega \omega 3+\omega 32+\omega 22+1$, $\omega \omega 3+\omega 32+\omega 22+2$, $\omega \omega 3+\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 22+\omega$.

"$\omega \omega 3+\omega 32+\omega 22+\omega$, $\omega \omega 3+\omega 32+\omega 22+\omega +1$, $\omega \omega 3+\omega 32+\omega 22+\omega +2$, $\omega \omega 3+\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega 3+\omega 32+\omega 22+\omega 2$, $\omega \omega 3+\omega 32+\omega 22+\omega 2+1$, $\omega \omega 3+\omega 32+\omega 22+\omega 2+2$, $\omega \omega 3+\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega 3+\omega 32+\omega 22+\omega 3$, $\omega \omega 3+\omega 32+\omega 22+\omega 3+1$, $\omega \omega 3+\omega 32+\omega 22+\omega 3+2$, $\omega \omega 3+\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 22+\omega 2$.

"$\omega \omega 3+\omega 32+\omega 23$, $\omega \omega 3+\omega 32+\omega 23+1$, $\omega \omega 3+\omega 32+\omega 23+2$, $\omega \omega 3+\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 23+\omega$.

"$\omega \omega 3+\omega 32+\omega 23+\omega$, $\omega \omega 3+\omega 32+\omega 23+\omega +1$, $\omega \omega 3+\omega 32+\omega 23+\omega +2$, $\omega \omega 3+\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega 3+\omega 32+\omega 23+\omega 2$, $\omega \omega 3+\omega 32+\omega 23+\omega 2+1$, $\omega \omega 3+\omega 32+\omega 23+\omega 2+2$, $\omega \omega 3+\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega 3+\omega 32+\omega 23+\omega 3$, $\omega \omega 3+\omega 32+\omega 23+\omega 3+1$, $\omega \omega 3+\omega 32+\omega 23+\omega 3+2$, $\omega \omega 3+\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 32+\omega 3$.

"$\omega \omega 3+\omega 33$, $\omega \omega 3+\omega 33+1$, $\omega \omega 3+\omega 33+2$, $\omega \omega 3+\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega$.

"$\omega \omega 3+\omega 33+\omega$, $\omega \omega 3+\omega 33+\omega +1$, $\omega \omega 3+\omega 33+\omega +2$, $\omega \omega 3+\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega +\omega$.

"$\omega \omega 3+\omega 33+\omega 2$, $\omega \omega 3+\omega 33+\omega 2+1$, $\omega \omega 3+\omega 33+\omega 2+2$, $\omega \omega 3+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 2+\omega$.

"$\omega \omega 3+\omega 33+\omega 3$, $\omega \omega 3+\omega 33+\omega 3+1$, $\omega \omega 3+\omega 33+\omega 3+2$, $\omega \omega 3+\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 2$.

"$\omega \omega 3+\omega 33+\omega 2$, $\omega \omega 3+\omega 33+\omega 2+1$, $\omega \omega 3+\omega 33+\omega 2+2$, $\omega \omega 3+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 2+\omega$.

"$\omega \omega 3+\omega 33+\omega 2+\omega$, $\omega \omega 3+\omega 33+\omega 2+\omega +1$, $\omega \omega 3+\omega 33+\omega 2+\omega +2$, $\omega \omega 3+\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega 3+\omega 33+\omega 2+\omega 2$, $\omega \omega 3+\omega 33+\omega 2+\omega 2+1$, $\omega \omega 3+\omega 33+\omega 2+\omega 2+2$, $\omega \omega 3+\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega 3+\omega 33+\omega 2+\omega 3$, $\omega \omega 3+\omega 33+\omega 2+\omega 3+1$, $\omega \omega 3+\omega 33+\omega 2+\omega 3+2$, $\omega \omega 3+\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 2+\omega 2$.

"$\omega \omega 3+\omega 33+\omega 22$, $\omega \omega 3+\omega 33+\omega 22+1$, $\omega \omega 3+\omega 33+\omega 22+2$, $\omega \omega 3+\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 22+\omega$.

"$\omega \omega 3+\omega 33+\omega 22+\omega$, $\omega \omega 3+\omega 33+\omega 22+\omega +1$, $\omega \omega 3+\omega 33+\omega 22+\omega +2$, $\omega \omega 3+\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega 3+\omega 33+\omega 22+\omega 2$, $\omega \omega 3+\omega 33+\omega 22+\omega 2+1$, $\omega \omega 3+\omega 33+\omega 22+\omega 2+2$, $\omega \omega 3+\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega 3+\omega 33+\omega 22+\omega 3$, $\omega \omega 3+\omega 33+\omega 22+\omega 3+1$, $\omega \omega 3+\omega 33+\omega 22+\omega 3+2$, $\omega \omega 3+\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 22+\omega 2$.

"$\omega \omega 3+\omega 33+\omega 23$, $\omega \omega 3+\omega 33+\omega 23+1$, $\omega \omega 3+\omega 33+\omega 23+2$, $\omega \omega 3+\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 23+\omega$.

"$\omega \omega 3+\omega 33+\omega 23+\omega$, $\omega \omega 3+\omega 33+\omega 23+\omega +1$, $\omega \omega 3+\omega 33+\omega 23+\omega +2$, $\omega \omega 3+\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega 3+\omega 33+\omega 23+\omega 2$, $\omega \omega 3+\omega 33+\omega 23+\omega 2+1$, $\omega \omega 3+\omega 33+\omega 23+\omega 2+2$, $\omega \omega 3+\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega 3+\omega 33+\omega 23+\omega 3$, $\omega \omega 3+\omega 33+\omega 23+\omega 3+1$, $\omega \omega 3+\omega 33+\omega 23+\omega 3+2$, $\omega \omega 3+\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega 3+\omega 33+\omega 3$.

"$\omega \omega +1$, $\omega \omega +1+1$, $\omega \omega +1+2$, $\omega \omega +1+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega$.

"$\omega \omega +1+\omega$, $\omega \omega +1+\omega +1$, $\omega \omega +1+\omega +2$, $\omega \omega +1+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega +\omega$.

"$\omega \omega +1+\omega 2$, $\omega \omega +1+\omega 2+1$, $\omega \omega +1+\omega 2+2$, $\omega \omega +1+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 2+\omega$.

"$\omega \omega +1+\omega 3$, $\omega \omega +1+\omega 3+1$, $\omega \omega +1+\omega 3+2$, $\omega \omega +1+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 2$.

"$\omega \omega +1+\omega 2$, $\omega \omega +1+\omega 2+1$, $\omega \omega +1+\omega 2+2$, $\omega \omega +1+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 2+\omega$.

"$\omega \omega +1+\omega 2+\omega$, $\omega \omega +1+\omega 2+\omega +1$, $\omega \omega +1+\omega 2+\omega +2$, $\omega \omega +1+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 2+\omega +\omega$.

"$\omega \omega +1+\omega 2+\omega 2$, $\omega \omega +1+\omega 2+\omega 2+1$, $\omega \omega +1+\omega 2+\omega 2+2$, $\omega \omega +1+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 2+\omega 2+\omega$.

"$\omega \omega +1+\omega 2+\omega 3$, $\omega \omega +1+\omega 2+\omega 3+1$, $\omega \omega +1+\omega 2+\omega 3+2$, $\omega \omega +1+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 2+\omega 2$.

"$\omega \omega +1+\omega 22$, $\omega \omega +1+\omega 22+1$, $\omega \omega +1+\omega 22+2$, $\omega \omega +1+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 22+\omega$.

"$\omega \omega +1+\omega 22+\omega$, $\omega \omega +1+\omega 22+\omega +1$, $\omega \omega +1+\omega 22+\omega +2$, $\omega \omega +1+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 22+\omega +\omega$.

"$\omega \omega +1+\omega 22+\omega 2$, $\omega \omega +1+\omega 22+\omega 2+1$, $\omega \omega +1+\omega 22+\omega 2+2$, $\omega \omega +1+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 22+\omega 2+\omega$.

"$\omega \omega +1+\omega 22+\omega 3$, $\omega \omega +1+\omega 22+\omega 3+1$, $\omega \omega +1+\omega 22+\omega 3+2$, $\omega \omega +1+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 22+\omega 2$.

"$\omega \omega +1+\omega 23$, $\omega \omega +1+\omega 23+1$, $\omega \omega +1+\omega 23+2$, $\omega \omega +1+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 23+\omega$.

"$\omega \omega +1+\omega 23+\omega$, $\omega \omega +1+\omega 23+\omega +1$, $\omega \omega +1+\omega 23+\omega +2$, $\omega \omega +1+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 23+\omega +\omega$.

"$\omega \omega +1+\omega 23+\omega 2$, $\omega \omega +1+\omega 23+\omega 2+1$, $\omega \omega +1+\omega 23+\omega 2+2$, $\omega \omega +1+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 23+\omega 2+\omega$.

"$\omega \omega +1+\omega 23+\omega 3$, $\omega \omega +1+\omega 23+\omega 3+1$, $\omega \omega +1+\omega 23+\omega 3+2$, $\omega \omega +1+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3$.

"$\omega \omega +1+\omega 3$, $\omega \omega +1+\omega 3+1$, $\omega \omega +1+\omega 3+2$, $\omega \omega +1+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega$.

"$\omega \omega +1+\omega 3+\omega$, $\omega \omega +1+\omega 3+\omega +1$, $\omega \omega +1+\omega 3+\omega +2$, $\omega \omega +1+\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega +\omega$.

"$\omega \omega +1+\omega 3+\omega 2$, $\omega \omega +1+\omega 3+\omega 2+1$, $\omega \omega +1+\omega 3+\omega 2+2$, $\omega \omega +1+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 2+\omega$.

"$\omega \omega +1+\omega 3+\omega 3$, $\omega \omega +1+\omega 3+\omega 3+1$, $\omega \omega +1+\omega 3+\omega 3+2$, $\omega \omega +1+\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 2$.

"$\omega \omega +1+\omega 3+\omega 2$, $\omega \omega +1+\omega 3+\omega 2+1$, $\omega \omega +1+\omega 3+\omega 2+2$, $\omega \omega +1+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 2+\omega$.

"$\omega \omega +1+\omega 3+\omega 2+\omega$, $\omega \omega +1+\omega 3+\omega 2+\omega +1$, $\omega \omega +1+\omega 3+\omega 2+\omega +2$, $\omega \omega +1+\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega +1+\omega 3+\omega 2+\omega 2$, $\omega \omega +1+\omega 3+\omega 2+\omega 2+1$, $\omega \omega +1+\omega 3+\omega 2+\omega 2+2$, $\omega \omega +1+\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega +1+\omega 3+\omega 2+\omega 3$, $\omega \omega +1+\omega 3+\omega 2+\omega 3+1$, $\omega \omega +1+\omega 3+\omega 2+\omega 3+2$, $\omega \omega +1+\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 2+\omega 2$.

"$\omega \omega +1+\omega 3+\omega 22$, $\omega \omega +1+\omega 3+\omega 22+1$, $\omega \omega +1+\omega 3+\omega 22+2$, $\omega \omega +1+\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 22+\omega$.

"$\omega \omega +1+\omega 3+\omega 22+\omega$, $\omega \omega +1+\omega 3+\omega 22+\omega +1$, $\omega \omega +1+\omega 3+\omega 22+\omega +2$, $\omega \omega +1+\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega +1+\omega 3+\omega 22+\omega 2$, $\omega \omega +1+\omega 3+\omega 22+\omega 2+1$, $\omega \omega +1+\omega 3+\omega 22+\omega 2+2$, $\omega \omega +1+\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega +1+\omega 3+\omega 22+\omega 3$, $\omega \omega +1+\omega 3+\omega 22+\omega 3+1$, $\omega \omega +1+\omega 3+\omega 22+\omega 3+2$, $\omega \omega +1+\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 22+\omega 2$.

"$\omega \omega +1+\omega 3+\omega 23$, $\omega \omega +1+\omega 3+\omega 23+1$, $\omega \omega +1+\omega 3+\omega 23+2$, $\omega \omega +1+\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 23+\omega$.

"$\omega \omega +1+\omega 3+\omega 23+\omega$, $\omega \omega +1+\omega 3+\omega 23+\omega +1$, $\omega \omega +1+\omega 3+\omega 23+\omega +2$, $\omega \omega +1+\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega +1+\omega 3+\omega 23+\omega 2$, $\omega \omega +1+\omega 3+\omega 23+\omega 2+1$, $\omega \omega +1+\omega 3+\omega 23+\omega 2+2$, $\omega \omega +1+\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega +1+\omega 3+\omega 23+\omega 3$, $\omega \omega +1+\omega 3+\omega 23+\omega 3+1$, $\omega \omega +1+\omega 3+\omega 23+\omega 3+2$, $\omega \omega +1+\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 3+\omega 3$.

"$\omega \omega +1+\omega 32$, $\omega \omega +1+\omega 32+1$, $\omega \omega +1+\omega 32+2$, $\omega \omega +1+\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega$.

"$\omega \omega +1+\omega 32+\omega$, $\omega \omega +1+\omega 32+\omega +1$, $\omega \omega +1+\omega 32+\omega +2$, $\omega \omega +1+\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega +\omega$.

"$\omega \omega +1+\omega 32+\omega 2$, $\omega \omega +1+\omega 32+\omega 2+1$, $\omega \omega +1+\omega 32+\omega 2+2$, $\omega \omega +1+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 2+\omega$.

"$\omega \omega +1+\omega 32+\omega 3$, $\omega \omega +1+\omega 32+\omega 3+1$, $\omega \omega +1+\omega 32+\omega 3+2$, $\omega \omega +1+\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 2$.

"$\omega \omega +1+\omega 32+\omega 2$, $\omega \omega +1+\omega 32+\omega 2+1$, $\omega \omega +1+\omega 32+\omega 2+2$, $\omega \omega +1+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 2+\omega$.

"$\omega \omega +1+\omega 32+\omega 2+\omega$, $\omega \omega +1+\omega 32+\omega 2+\omega +1$, $\omega \omega +1+\omega 32+\omega 2+\omega +2$, $\omega \omega +1+\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega +1+\omega 32+\omega 2+\omega 2$, $\omega \omega +1+\omega 32+\omega 2+\omega 2+1$, $\omega \omega +1+\omega 32+\omega 2+\omega 2+2$, $\omega \omega +1+\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega +1+\omega 32+\omega 2+\omega 3$, $\omega \omega +1+\omega 32+\omega 2+\omega 3+1$, $\omega \omega +1+\omega 32+\omega 2+\omega 3+2$, $\omega \omega +1+\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 2+\omega 2$.

"$\omega \omega +1+\omega 32+\omega 22$, $\omega \omega +1+\omega 32+\omega 22+1$, $\omega \omega +1+\omega 32+\omega 22+2$, $\omega \omega +1+\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 22+\omega$.

"$\omega \omega +1+\omega 32+\omega 22+\omega$, $\omega \omega +1+\omega 32+\omega 22+\omega +1$, $\omega \omega +1+\omega 32+\omega 22+\omega +2$, $\omega \omega +1+\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega +1+\omega 32+\omega 22+\omega 2$, $\omega \omega +1+\omega 32+\omega 22+\omega 2+1$, $\omega \omega +1+\omega 32+\omega 22+\omega 2+2$, $\omega \omega +1+\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega +1+\omega 32+\omega 22+\omega 3$, $\omega \omega +1+\omega 32+\omega 22+\omega 3+1$, $\omega \omega +1+\omega 32+\omega 22+\omega 3+2$, $\omega \omega +1+\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 22+\omega 2$.

"$\omega \omega +1+\omega 32+\omega 23$, $\omega \omega +1+\omega 32+\omega 23+1$, $\omega \omega +1+\omega 32+\omega 23+2$, $\omega \omega +1+\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 23+\omega$.

"$\omega \omega +1+\omega 32+\omega 23+\omega$, $\omega \omega +1+\omega 32+\omega 23+\omega +1$, $\omega \omega +1+\omega 32+\omega 23+\omega +2$, $\omega \omega +1+\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega +1+\omega 32+\omega 23+\omega 2$, $\omega \omega +1+\omega 32+\omega 23+\omega 2+1$, $\omega \omega +1+\omega 32+\omega 23+\omega 2+2$, $\omega \omega +1+\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega +1+\omega 32+\omega 23+\omega 3$, $\omega \omega +1+\omega 32+\omega 23+\omega 3+1$, $\omega \omega +1+\omega 32+\omega 23+\omega 3+2$, $\omega \omega +1+\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 32+\omega 3$.

"$\omega \omega +1+\omega 33$, $\omega \omega +1+\omega 33+1$, $\omega \omega +1+\omega 33+2$, $\omega \omega +1+\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega$.

"$\omega \omega +1+\omega 33+\omega$, $\omega \omega +1+\omega 33+\omega +1$, $\omega \omega +1+\omega 33+\omega +2$, $\omega \omega +1+\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega +\omega$.

"$\omega \omega +1+\omega 33+\omega 2$, $\omega \omega +1+\omega 33+\omega 2+1$, $\omega \omega +1+\omega 33+\omega 2+2$, $\omega \omega +1+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 2+\omega$.

"$\omega \omega +1+\omega 33+\omega 3$, $\omega \omega +1+\omega 33+\omega 3+1$, $\omega \omega +1+\omega 33+\omega 3+2$, $\omega \omega +1+\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 2$.

"$\omega \omega +1+\omega 33+\omega 2$, $\omega \omega +1+\omega 33+\omega 2+1$, $\omega \omega +1+\omega 33+\omega 2+2$, $\omega \omega +1+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 2+\omega$.

"$\omega \omega +1+\omega 33+\omega 2+\omega$, $\omega \omega +1+\omega 33+\omega 2+\omega +1$, $\omega \omega +1+\omega 33+\omega 2+\omega +2$, $\omega \omega +1+\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega +1+\omega 33+\omega 2+\omega 2$, $\omega \omega +1+\omega 33+\omega 2+\omega 2+1$, $\omega \omega +1+\omega 33+\omega 2+\omega 2+2$, $\omega \omega +1+\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega +1+\omega 33+\omega 2+\omega 3$, $\omega \omega +1+\omega 33+\omega 2+\omega 3+1$, $\omega \omega +1+\omega 33+\omega 2+\omega 3+2$, $\omega \omega +1+\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 2+\omega 2$.

"$\omega \omega +1+\omega 33+\omega 22$, $\omega \omega +1+\omega 33+\omega 22+1$, $\omega \omega +1+\omega 33+\omega 22+2$, $\omega \omega +1+\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 22+\omega$.

"$\omega \omega +1+\omega 33+\omega 22+\omega$, $\omega \omega +1+\omega 33+\omega 22+\omega +1$, $\omega \omega +1+\omega 33+\omega 22+\omega +2$, $\omega \omega +1+\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega +1+\omega 33+\omega 22+\omega 2$, $\omega \omega +1+\omega 33+\omega 22+\omega 2+1$, $\omega \omega +1+\omega 33+\omega 22+\omega 2+2$, $\omega \omega +1+\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega +1+\omega 33+\omega 22+\omega 3$, $\omega \omega +1+\omega 33+\omega 22+\omega 3+1$, $\omega \omega +1+\omega 33+\omega 22+\omega 3+2$, $\omega \omega +1+\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 22+\omega 2$.

"$\omega \omega +1+\omega 33+\omega 23$, $\omega \omega +1+\omega 33+\omega 23+1$, $\omega \omega +1+\omega 33+\omega 23+2$, $\omega \omega +1+\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 23+\omega$.

"$\omega \omega +1+\omega 33+\omega 23+\omega$, $\omega \omega +1+\omega 33+\omega 23+\omega +1$, $\omega \omega +1+\omega 33+\omega 23+\omega +2$, $\omega \omega +1+\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega +1+\omega 33+\omega 23+\omega 2$, $\omega \omega +1+\omega 33+\omega 23+\omega 2+1$, $\omega \omega +1+\omega 33+\omega 23+\omega 2+2$, $\omega \omega +1+\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega +1+\omega 33+\omega 23+\omega 3$, $\omega \omega +1+\omega 33+\omega 23+\omega 3+1$, $\omega \omega +1+\omega 33+\omega 23+\omega 3+2$, $\omega \omega +1+\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +1+\omega 33+\omega 3$.

"$\omega \omega +12$, $\omega \omega +12+1$, $\omega \omega +12+2$, $\omega \omega +12+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega$.

"$\omega \omega +12+\omega$, $\omega \omega +12+\omega +1$, $\omega \omega +12+\omega +2$, $\omega \omega +12+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega +\omega$.

"$\omega \omega +12+\omega 2$, $\omega \omega +12+\omega 2+1$, $\omega \omega +12+\omega 2+2$, $\omega \omega +12+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 2+\omega$.

"$\omega \omega +12+\omega 3$, $\omega \omega +12+\omega 3+1$, $\omega \omega +12+\omega 3+2$, $\omega \omega +12+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 2$.

"$\omega \omega +12+\omega 2$, $\omega \omega +12+\omega 2+1$, $\omega \omega +12+\omega 2+2$, $\omega \omega +12+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 2+\omega$.

"$\omega \omega +12+\omega 2+\omega$, $\omega \omega +12+\omega 2+\omega +1$, $\omega \omega +12+\omega 2+\omega +2$, $\omega \omega +12+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 2+\omega +\omega$.

"$\omega \omega +12+\omega 2+\omega 2$, $\omega \omega +12+\omega 2+\omega 2+1$, $\omega \omega +12+\omega 2+\omega 2+2$, $\omega \omega +12+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 2+\omega 2+\omega$.

"$\omega \omega +12+\omega 2+\omega 3$, $\omega \omega +12+\omega 2+\omega 3+1$, $\omega \omega +12+\omega 2+\omega 3+2$, $\omega \omega +12+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 2+\omega 2$.

"$\omega \omega +12+\omega 22$, $\omega \omega +12+\omega 22+1$, $\omega \omega +12+\omega 22+2$, $\omega \omega +12+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 22+\omega$.

"$\omega \omega +12+\omega 22+\omega$, $\omega \omega +12+\omega 22+\omega +1$, $\omega \omega +12+\omega 22+\omega +2$, $\omega \omega +12+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 22+\omega +\omega$.

"$\omega \omega +12+\omega 22+\omega 2$, $\omega \omega +12+\omega 22+\omega 2+1$, $\omega \omega +12+\omega 22+\omega 2+2$, $\omega \omega +12+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 22+\omega 2+\omega$.

"$\omega \omega +12+\omega 22+\omega 3$, $\omega \omega +12+\omega 22+\omega 3+1$, $\omega \omega +12+\omega 22+\omega 3+2$, $\omega \omega +12+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 22+\omega 2$.

"$\omega \omega +12+\omega 23$, $\omega \omega +12+\omega 23+1$, $\omega \omega +12+\omega 23+2$, $\omega \omega +12+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 23+\omega$.

"$\omega \omega +12+\omega 23+\omega$, $\omega \omega +12+\omega 23+\omega +1$, $\omega \omega +12+\omega 23+\omega +2$, $\omega \omega +12+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 23+\omega +\omega$.

"$\omega \omega +12+\omega 23+\omega 2$, $\omega \omega +12+\omega 23+\omega 2+1$, $\omega \omega +12+\omega 23+\omega 2+2$, $\omega \omega +12+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 23+\omega 2+\omega$.

"$\omega \omega +12+\omega 23+\omega 3$, $\omega \omega +12+\omega 23+\omega 3+1$, $\omega \omega +12+\omega 23+\omega 3+2$, $\omega \omega +12+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3$.

"$\omega \omega +12+\omega 3$, $\omega \omega +12+\omega 3+1$, $\omega \omega +12+\omega 3+2$, $\omega \omega +12+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega$.

"$\omega \omega +12+\omega 3+\omega$, $\omega \omega +12+\omega 3+\omega +1$, $\omega \omega +12+\omega 3+\omega +2$, $\omega \omega +12+\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega +\omega$.

"$\omega \omega +12+\omega 3+\omega 2$, $\omega \omega +12+\omega 3+\omega 2+1$, $\omega \omega +12+\omega 3+\omega 2+2$, $\omega \omega +12+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 2+\omega$.

"$\omega \omega +12+\omega 3+\omega 3$, $\omega \omega +12+\omega 3+\omega 3+1$, $\omega \omega +12+\omega 3+\omega 3+2$, $\omega \omega +12+\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 2$.

"$\omega \omega +12+\omega 3+\omega 2$, $\omega \omega +12+\omega 3+\omega 2+1$, $\omega \omega +12+\omega 3+\omega 2+2$, $\omega \omega +12+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 2+\omega$.

"$\omega \omega +12+\omega 3+\omega 2+\omega$, $\omega \omega +12+\omega 3+\omega 2+\omega +1$, $\omega \omega +12+\omega 3+\omega 2+\omega +2$, $\omega \omega +12+\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega +12+\omega 3+\omega 2+\omega 2$, $\omega \omega +12+\omega 3+\omega 2+\omega 2+1$, $\omega \omega +12+\omega 3+\omega 2+\omega 2+2$, $\omega \omega +12+\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega +12+\omega 3+\omega 2+\omega 3$, $\omega \omega +12+\omega 3+\omega 2+\omega 3+1$, $\omega \omega +12+\omega 3+\omega 2+\omega 3+2$, $\omega \omega +12+\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 2+\omega 2$.

"$\omega \omega +12+\omega 3+\omega 22$, $\omega \omega +12+\omega 3+\omega 22+1$, $\omega \omega +12+\omega 3+\omega 22+2$, $\omega \omega +12+\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 22+\omega$.

"$\omega \omega +12+\omega 3+\omega 22+\omega$, $\omega \omega +12+\omega 3+\omega 22+\omega +1$, $\omega \omega +12+\omega 3+\omega 22+\omega +2$, $\omega \omega +12+\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega +12+\omega 3+\omega 22+\omega 2$, $\omega \omega +12+\omega 3+\omega 22+\omega 2+1$, $\omega \omega +12+\omega 3+\omega 22+\omega 2+2$, $\omega \omega +12+\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega +12+\omega 3+\omega 22+\omega 3$, $\omega \omega +12+\omega 3+\omega 22+\omega 3+1$, $\omega \omega +12+\omega 3+\omega 22+\omega 3+2$, $\omega \omega +12+\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 22+\omega 2$.

"$\omega \omega +12+\omega 3+\omega 23$, $\omega \omega +12+\omega 3+\omega 23+1$, $\omega \omega +12+\omega 3+\omega 23+2$, $\omega \omega +12+\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 23+\omega$.

"$\omega \omega +12+\omega 3+\omega 23+\omega$, $\omega \omega +12+\omega 3+\omega 23+\omega +1$, $\omega \omega +12+\omega 3+\omega 23+\omega +2$, $\omega \omega +12+\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega +12+\omega 3+\omega 23+\omega 2$, $\omega \omega +12+\omega 3+\omega 23+\omega 2+1$, $\omega \omega +12+\omega 3+\omega 23+\omega 2+2$, $\omega \omega +12+\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega +12+\omega 3+\omega 23+\omega 3$, $\omega \omega +12+\omega 3+\omega 23+\omega 3+1$, $\omega \omega +12+\omega 3+\omega 23+\omega 3+2$, $\omega \omega +12+\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 3+\omega 3$.

"$\omega \omega +12+\omega 32$, $\omega \omega +12+\omega 32+1$, $\omega \omega +12+\omega 32+2$, $\omega \omega +12+\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega$.

"$\omega \omega +12+\omega 32+\omega$, $\omega \omega +12+\omega 32+\omega +1$, $\omega \omega +12+\omega 32+\omega +2$, $\omega \omega +12+\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega +\omega$.

"$\omega \omega +12+\omega 32+\omega 2$, $\omega \omega +12+\omega 32+\omega 2+1$, $\omega \omega +12+\omega 32+\omega 2+2$, $\omega \omega +12+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 2+\omega$.

"$\omega \omega +12+\omega 32+\omega 3$, $\omega \omega +12+\omega 32+\omega 3+1$, $\omega \omega +12+\omega 32+\omega 3+2$, $\omega \omega +12+\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 2$.

"$\omega \omega +12+\omega 32+\omega 2$, $\omega \omega +12+\omega 32+\omega 2+1$, $\omega \omega +12+\omega 32+\omega 2+2$, $\omega \omega +12+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 2+\omega$.

"$\omega \omega +12+\omega 32+\omega 2+\omega$, $\omega \omega +12+\omega 32+\omega 2+\omega +1$, $\omega \omega +12+\omega 32+\omega 2+\omega +2$, $\omega \omega +12+\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega +12+\omega 32+\omega 2+\omega 2$, $\omega \omega +12+\omega 32+\omega 2+\omega 2+1$, $\omega \omega +12+\omega 32+\omega 2+\omega 2+2$, $\omega \omega +12+\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega +12+\omega 32+\omega 2+\omega 3$, $\omega \omega +12+\omega 32+\omega 2+\omega 3+1$, $\omega \omega +12+\omega 32+\omega 2+\omega 3+2$, $\omega \omega +12+\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 2+\omega 2$.

"$\omega \omega +12+\omega 32+\omega 22$, $\omega \omega +12+\omega 32+\omega 22+1$, $\omega \omega +12+\omega 32+\omega 22+2$, $\omega \omega +12+\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 22+\omega$.

"$\omega \omega +12+\omega 32+\omega 22+\omega$, $\omega \omega +12+\omega 32+\omega 22+\omega +1$, $\omega \omega +12+\omega 32+\omega 22+\omega +2$, $\omega \omega +12+\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega +12+\omega 32+\omega 22+\omega 2$, $\omega \omega +12+\omega 32+\omega 22+\omega 2+1$, $\omega \omega +12+\omega 32+\omega 22+\omega 2+2$, $\omega \omega +12+\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega +12+\omega 32+\omega 22+\omega 3$, $\omega \omega +12+\omega 32+\omega 22+\omega 3+1$, $\omega \omega +12+\omega 32+\omega 22+\omega 3+2$, $\omega \omega +12+\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 22+\omega 2$.

"$\omega \omega +12+\omega 32+\omega 23$, $\omega \omega +12+\omega 32+\omega 23+1$, $\omega \omega +12+\omega 32+\omega 23+2$, $\omega \omega +12+\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 23+\omega$.

"$\omega \omega +12+\omega 32+\omega 23+\omega$, $\omega \omega +12+\omega 32+\omega 23+\omega +1$, $\omega \omega +12+\omega 32+\omega 23+\omega +2$, $\omega \omega +12+\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega +12+\omega 32+\omega 23+\omega 2$, $\omega \omega +12+\omega 32+\omega 23+\omega 2+1$, $\omega \omega +12+\omega 32+\omega 23+\omega 2+2$, $\omega \omega +12+\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega +12+\omega 32+\omega 23+\omega 3$, $\omega \omega +12+\omega 32+\omega 23+\omega 3+1$, $\omega \omega +12+\omega 32+\omega 23+\omega 3+2$, $\omega \omega +12+\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 32+\omega 3$.

"$\omega \omega +12+\omega 33$, $\omega \omega +12+\omega 33+1$, $\omega \omega +12+\omega 33+2$, $\omega \omega +12+\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega$.

"$\omega \omega +12+\omega 33+\omega$, $\omega \omega +12+\omega 33+\omega +1$, $\omega \omega +12+\omega 33+\omega +2$, $\omega \omega +12+\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega +\omega$.

"$\omega \omega +12+\omega 33+\omega 2$, $\omega \omega +12+\omega 33+\omega 2+1$, $\omega \omega +12+\omega 33+\omega 2+2$, $\omega \omega +12+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 2+\omega$.

"$\omega \omega +12+\omega 33+\omega 3$, $\omega \omega +12+\omega 33+\omega 3+1$, $\omega \omega +12+\omega 33+\omega 3+2$, $\omega \omega +12+\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 2$.

"$\omega \omega +12+\omega 33+\omega 2$, $\omega \omega +12+\omega 33+\omega 2+1$, $\omega \omega +12+\omega 33+\omega 2+2$, $\omega \omega +12+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 2+\omega$.

"$\omega \omega +12+\omega 33+\omega 2+\omega$, $\omega \omega +12+\omega 33+\omega 2+\omega +1$, $\omega \omega +12+\omega 33+\omega 2+\omega +2$, $\omega \omega +12+\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega +12+\omega 33+\omega 2+\omega 2$, $\omega \omega +12+\omega 33+\omega 2+\omega 2+1$, $\omega \omega +12+\omega 33+\omega 2+\omega 2+2$, $\omega \omega +12+\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega +12+\omega 33+\omega 2+\omega 3$, $\omega \omega +12+\omega 33+\omega 2+\omega 3+1$, $\omega \omega +12+\omega 33+\omega 2+\omega 3+2$, $\omega \omega +12+\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 2+\omega 2$.

"$\omega \omega +12+\omega 33+\omega 22$, $\omega \omega +12+\omega 33+\omega 22+1$, $\omega \omega +12+\omega 33+\omega 22+2$, $\omega \omega +12+\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 22+\omega$.

"$\omega \omega +12+\omega 33+\omega 22+\omega$, $\omega \omega +12+\omega 33+\omega 22+\omega +1$, $\omega \omega +12+\omega 33+\omega 22+\omega +2$, $\omega \omega +12+\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega +12+\omega 33+\omega 22+\omega 2$, $\omega \omega +12+\omega 33+\omega 22+\omega 2+1$, $\omega \omega +12+\omega 33+\omega 22+\omega 2+2$, $\omega \omega +12+\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega +12+\omega 33+\omega 22+\omega 3$, $\omega \omega +12+\omega 33+\omega 22+\omega 3+1$, $\omega \omega +12+\omega 33+\omega 22+\omega 3+2$, $\omega \omega +12+\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 22+\omega 2$.

"$\omega \omega +12+\omega 33+\omega 23$, $\omega \omega +12+\omega 33+\omega 23+1$, $\omega \omega +12+\omega 33+\omega 23+2$, $\omega \omega +12+\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 23+\omega$.

"$\omega \omega +12+\omega 33+\omega 23+\omega$, $\omega \omega +12+\omega 33+\omega 23+\omega +1$, $\omega \omega +12+\omega 33+\omega 23+\omega +2$, $\omega \omega +12+\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega +12+\omega 33+\omega 23+\omega 2$, $\omega \omega +12+\omega 33+\omega 23+\omega 2+1$, $\omega \omega +12+\omega 33+\omega 23+\omega 2+2$, $\omega \omega +12+\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega +12+\omega 33+\omega 23+\omega 3$, $\omega \omega +12+\omega 33+\omega 23+\omega 3+1$, $\omega \omega +12+\omega 33+\omega 23+\omega 3+2$, $\omega \omega +12+\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +12+\omega 33+\omega 3$.

"$\omega \omega +13$, $\omega \omega +13+1$, $\omega \omega +13+2$, $\omega \omega +13+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega$.

"$\omega \omega +13+\omega$, $\omega \omega +13+\omega +1$, $\omega \omega +13+\omega +2$, $\omega \omega +13+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega +\omega$.

"$\omega \omega +13+\omega 2$, $\omega \omega +13+\omega 2+1$, $\omega \omega +13+\omega 2+2$, $\omega \omega +13+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 2+\omega$.

"$\omega \omega +13+\omega 3$, $\omega \omega +13+\omega 3+1$, $\omega \omega +13+\omega 3+2$, $\omega \omega +13+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 2$.

"$\omega \omega +13+\omega 2$, $\omega \omega +13+\omega 2+1$, $\omega \omega +13+\omega 2+2$, $\omega \omega +13+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 2+\omega$.

"$\omega \omega +13+\omega 2+\omega$, $\omega \omega +13+\omega 2+\omega +1$, $\omega \omega +13+\omega 2+\omega +2$, $\omega \omega +13+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 2+\omega +\omega$.

"$\omega \omega +13+\omega 2+\omega 2$, $\omega \omega +13+\omega 2+\omega 2+1$, $\omega \omega +13+\omega 2+\omega 2+2$, $\omega \omega +13+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 2+\omega 2+\omega$.

"$\omega \omega +13+\omega 2+\omega 3$, $\omega \omega +13+\omega 2+\omega 3+1$, $\omega \omega +13+\omega 2+\omega 3+2$, $\omega \omega +13+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 2+\omega 2$.

"$\omega \omega +13+\omega 22$, $\omega \omega +13+\omega 22+1$, $\omega \omega +13+\omega 22+2$, $\omega \omega +13+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 22+\omega$.

"$\omega \omega +13+\omega 22+\omega$, $\omega \omega +13+\omega 22+\omega +1$, $\omega \omega +13+\omega 22+\omega +2$, $\omega \omega +13+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 22+\omega +\omega$.

"$\omega \omega +13+\omega 22+\omega 2$, $\omega \omega +13+\omega 22+\omega 2+1$, $\omega \omega +13+\omega 22+\omega 2+2$, $\omega \omega +13+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 22+\omega 2+\omega$.

"$\omega \omega +13+\omega 22+\omega 3$, $\omega \omega +13+\omega 22+\omega 3+1$, $\omega \omega +13+\omega 22+\omega 3+2$, $\omega \omega +13+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 22+\omega 2$.

"$\omega \omega +13+\omega 23$, $\omega \omega +13+\omega 23+1$, $\omega \omega +13+\omega 23+2$, $\omega \omega +13+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 23+\omega$.

"$\omega \omega +13+\omega 23+\omega$, $\omega \omega +13+\omega 23+\omega +1$, $\omega \omega +13+\omega 23+\omega +2$, $\omega \omega +13+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 23+\omega +\omega$.

"$\omega \omega +13+\omega 23+\omega 2$, $\omega \omega +13+\omega 23+\omega 2+1$, $\omega \omega +13+\omega 23+\omega 2+2$, $\omega \omega +13+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 23+\omega 2+\omega$.

"$\omega \omega +13+\omega 23+\omega 3$, $\omega \omega +13+\omega 23+\omega 3+1$, $\omega \omega +13+\omega 23+\omega 3+2$, $\omega \omega +13+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3$.

"$\omega \omega +13+\omega 3$, $\omega \omega +13+\omega 3+1$, $\omega \omega +13+\omega 3+2$, $\omega \omega +13+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega$.

"$\omega \omega +13+\omega 3+\omega$, $\omega \omega +13+\omega 3+\omega +1$, $\omega \omega +13+\omega 3+\omega +2$, $\omega \omega +13+\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega +\omega$.

"$\omega \omega +13+\omega 3+\omega 2$, $\omega \omega +13+\omega 3+\omega 2+1$, $\omega \omega +13+\omega 3+\omega 2+2$, $\omega \omega +13+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 2+\omega$.

"$\omega \omega +13+\omega 3+\omega 3$, $\omega \omega +13+\omega 3+\omega 3+1$, $\omega \omega +13+\omega 3+\omega 3+2$, $\omega \omega +13+\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 2$.

"$\omega \omega +13+\omega 3+\omega 2$, $\omega \omega +13+\omega 3+\omega 2+1$, $\omega \omega +13+\omega 3+\omega 2+2$, $\omega \omega +13+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 2+\omega$.

"$\omega \omega +13+\omega 3+\omega 2+\omega$, $\omega \omega +13+\omega 3+\omega 2+\omega +1$, $\omega \omega +13+\omega 3+\omega 2+\omega +2$, $\omega \omega +13+\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega +13+\omega 3+\omega 2+\omega 2$, $\omega \omega +13+\omega 3+\omega 2+\omega 2+1$, $\omega \omega +13+\omega 3+\omega 2+\omega 2+2$, $\omega \omega +13+\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega +13+\omega 3+\omega 2+\omega 3$, $\omega \omega +13+\omega 3+\omega 2+\omega 3+1$, $\omega \omega +13+\omega 3+\omega 2+\omega 3+2$, $\omega \omega +13+\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 2+\omega 2$.

"$\omega \omega +13+\omega 3+\omega 22$, $\omega \omega +13+\omega 3+\omega 22+1$, $\omega \omega +13+\omega 3+\omega 22+2$, $\omega \omega +13+\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 22+\omega$.

"$\omega \omega +13+\omega 3+\omega 22+\omega$, $\omega \omega +13+\omega 3+\omega 22+\omega +1$, $\omega \omega +13+\omega 3+\omega 22+\omega +2$, $\omega \omega +13+\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega +13+\omega 3+\omega 22+\omega 2$, $\omega \omega +13+\omega 3+\omega 22+\omega 2+1$, $\omega \omega +13+\omega 3+\omega 22+\omega 2+2$, $\omega \omega +13+\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega +13+\omega 3+\omega 22+\omega 3$, $\omega \omega +13+\omega 3+\omega 22+\omega 3+1$, $\omega \omega +13+\omega 3+\omega 22+\omega 3+2$, $\omega \omega +13+\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 22+\omega 2$.

"$\omega \omega +13+\omega 3+\omega 23$, $\omega \omega +13+\omega 3+\omega 23+1$, $\omega \omega +13+\omega 3+\omega 23+2$, $\omega \omega +13+\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 23+\omega$.

"$\omega \omega +13+\omega 3+\omega 23+\omega$, $\omega \omega +13+\omega 3+\omega 23+\omega +1$, $\omega \omega +13+\omega 3+\omega 23+\omega +2$, $\omega \omega +13+\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega +13+\omega 3+\omega 23+\omega 2$, $\omega \omega +13+\omega 3+\omega 23+\omega 2+1$, $\omega \omega +13+\omega 3+\omega 23+\omega 2+2$, $\omega \omega +13+\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega +13+\omega 3+\omega 23+\omega 3$, $\omega \omega +13+\omega 3+\omega 23+\omega 3+1$, $\omega \omega +13+\omega 3+\omega 23+\omega 3+2$, $\omega \omega +13+\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 3+\omega 3$.

"$\omega \omega +13+\omega 32$, $\omega \omega +13+\omega 32+1$, $\omega \omega +13+\omega 32+2$, $\omega \omega +13+\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega$.

"$\omega \omega +13+\omega 32+\omega$, $\omega \omega +13+\omega 32+\omega +1$, $\omega \omega +13+\omega 32+\omega +2$, $\omega \omega +13+\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega +\omega$.

"$\omega \omega +13+\omega 32+\omega 2$, $\omega \omega +13+\omega 32+\omega 2+1$, $\omega \omega +13+\omega 32+\omega 2+2$, $\omega \omega +13+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 2+\omega$.

"$\omega \omega +13+\omega 32+\omega 3$, $\omega \omega +13+\omega 32+\omega 3+1$, $\omega \omega +13+\omega 32+\omega 3+2$, $\omega \omega +13+\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 2$.

"$\omega \omega +13+\omega 32+\omega 2$, $\omega \omega +13+\omega 32+\omega 2+1$, $\omega \omega +13+\omega 32+\omega 2+2$, $\omega \omega +13+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 2+\omega$.

"$\omega \omega +13+\omega 32+\omega 2+\omega$, $\omega \omega +13+\omega 32+\omega 2+\omega +1$, $\omega \omega +13+\omega 32+\omega 2+\omega +2$, $\omega \omega +13+\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega +13+\omega 32+\omega 2+\omega 2$, $\omega \omega +13+\omega 32+\omega 2+\omega 2+1$, $\omega \omega +13+\omega 32+\omega 2+\omega 2+2$, $\omega \omega +13+\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega +13+\omega 32+\omega 2+\omega 3$, $\omega \omega +13+\omega 32+\omega 2+\omega 3+1$, $\omega \omega +13+\omega 32+\omega 2+\omega 3+2$, $\omega \omega +13+\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 2+\omega 2$.

"$\omega \omega +13+\omega 32+\omega 22$, $\omega \omega +13+\omega 32+\omega 22+1$, $\omega \omega +13+\omega 32+\omega 22+2$, $\omega \omega +13+\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 22+\omega$.

"$\omega \omega +13+\omega 32+\omega 22+\omega$, $\omega \omega +13+\omega 32+\omega 22+\omega +1$, $\omega \omega +13+\omega 32+\omega 22+\omega +2$, $\omega \omega +13+\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega +13+\omega 32+\omega 22+\omega 2$, $\omega \omega +13+\omega 32+\omega 22+\omega 2+1$, $\omega \omega +13+\omega 32+\omega 22+\omega 2+2$, $\omega \omega +13+\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega +13+\omega 32+\omega 22+\omega 3$, $\omega \omega +13+\omega 32+\omega 22+\omega 3+1$, $\omega \omega +13+\omega 32+\omega 22+\omega 3+2$, $\omega \omega +13+\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 22+\omega 2$.

"$\omega \omega +13+\omega 32+\omega 23$, $\omega \omega +13+\omega 32+\omega 23+1$, $\omega \omega +13+\omega 32+\omega 23+2$, $\omega \omega +13+\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 23+\omega$.

"$\omega \omega +13+\omega 32+\omega 23+\omega$, $\omega \omega +13+\omega 32+\omega 23+\omega +1$, $\omega \omega +13+\omega 32+\omega 23+\omega +2$, $\omega \omega +13+\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega +13+\omega 32+\omega 23+\omega 2$, $\omega \omega +13+\omega 32+\omega 23+\omega 2+1$, $\omega \omega +13+\omega 32+\omega 23+\omega 2+2$, $\omega \omega +13+\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega +13+\omega 32+\omega 23+\omega 3$, $\omega \omega +13+\omega 32+\omega 23+\omega 3+1$, $\omega \omega +13+\omega 32+\omega 23+\omega 3+2$, $\omega \omega +13+\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 32+\omega 3$.

"$\omega \omega +13+\omega 33$, $\omega \omega +13+\omega 33+1$, $\omega \omega +13+\omega 33+2$, $\omega \omega +13+\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega$.

"$\omega \omega +13+\omega 33+\omega$, $\omega \omega +13+\omega 33+\omega +1$, $\omega \omega +13+\omega 33+\omega +2$, $\omega \omega +13+\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega +\omega$.

"$\omega \omega +13+\omega 33+\omega 2$, $\omega \omega +13+\omega 33+\omega 2+1$, $\omega \omega +13+\omega 33+\omega 2+2$, $\omega \omega +13+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 2+\omega$.

"$\omega \omega +13+\omega 33+\omega 3$, $\omega \omega +13+\omega 33+\omega 3+1$, $\omega \omega +13+\omega 33+\omega 3+2$, $\omega \omega +13+\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 2$.

"$\omega \omega +13+\omega 33+\omega 2$, $\omega \omega +13+\omega 33+\omega 2+1$, $\omega \omega +13+\omega 33+\omega 2+2$, $\omega \omega +13+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 2+\omega$.

"$\omega \omega +13+\omega 33+\omega 2+\omega$, $\omega \omega +13+\omega 33+\omega 2+\omega +1$, $\omega \omega +13+\omega 33+\omega 2+\omega +2$, $\omega \omega +13+\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega +13+\omega 33+\omega 2+\omega 2$, $\omega \omega +13+\omega 33+\omega 2+\omega 2+1$, $\omega \omega +13+\omega 33+\omega 2+\omega 2+2$, $\omega \omega +13+\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega +13+\omega 33+\omega 2+\omega 3$, $\omega \omega +13+\omega 33+\omega 2+\omega 3+1$, $\omega \omega +13+\omega 33+\omega 2+\omega 3+2$, $\omega \omega +13+\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 2+\omega 2$.

"$\omega \omega +13+\omega 33+\omega 22$, $\omega \omega +13+\omega 33+\omega 22+1$, $\omega \omega +13+\omega 33+\omega 22+2$, $\omega \omega +13+\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 22+\omega$.

"$\omega \omega +13+\omega 33+\omega 22+\omega$, $\omega \omega +13+\omega 33+\omega 22+\omega +1$, $\omega \omega +13+\omega 33+\omega 22+\omega +2$, $\omega \omega +13+\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega +13+\omega 33+\omega 22+\omega 2$, $\omega \omega +13+\omega 33+\omega 22+\omega 2+1$, $\omega \omega +13+\omega 33+\omega 22+\omega 2+2$, $\omega \omega +13+\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega +13+\omega 33+\omega 22+\omega 3$, $\omega \omega +13+\omega 33+\omega 22+\omega 3+1$, $\omega \omega +13+\omega 33+\omega 22+\omega 3+2$, $\omega \omega +13+\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 22+\omega 2$.

"$\omega \omega +13+\omega 33+\omega 23$, $\omega \omega +13+\omega 33+\omega 23+1$, $\omega \omega +13+\omega 33+\omega 23+2$, $\omega \omega +13+\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 23+\omega$.

"$\omega \omega +13+\omega 33+\omega 23+\omega$, $\omega \omega +13+\omega 33+\omega 23+\omega +1$, $\omega \omega +13+\omega 33+\omega 23+\omega +2$, $\omega \omega +13+\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega +13+\omega 33+\omega 23+\omega 2$, $\omega \omega +13+\omega 33+\omega 23+\omega 2+1$, $\omega \omega +13+\omega 33+\omega 23+\omega 2+2$, $\omega \omega +13+\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega +13+\omega 33+\omega 23+\omega 3$, $\omega \omega +13+\omega 33+\omega 23+\omega 3+1$, $\omega \omega +13+\omega 33+\omega 23+\omega 3+2$, $\omega \omega +13+\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +13+\omega 33+\omega 3$.

"$\omega \omega +2$, $\omega \omega +2+1$, $\omega \omega +2+2$, $\omega \omega +2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega$.

"$\omega \omega +2+\omega$, $\omega \omega +2+\omega +1$, $\omega \omega +2+\omega +2$, $\omega \omega +2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega +\omega$.

"$\omega \omega +2+\omega 2$, $\omega \omega +2+\omega 2+1$, $\omega \omega +2+\omega 2+2$, $\omega \omega +2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 2+\omega$.

"$\omega \omega +2+\omega 3$, $\omega \omega +2+\omega 3+1$, $\omega \omega +2+\omega 3+2$, $\omega \omega +2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 2$.

"$\omega \omega +2+\omega 2$, $\omega \omega +2+\omega 2+1$, $\omega \omega +2+\omega 2+2$, $\omega \omega +2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 2+\omega$.

"$\omega \omega +2+\omega 2+\omega$, $\omega \omega +2+\omega 2+\omega +1$, $\omega \omega +2+\omega 2+\omega +2$, $\omega \omega +2+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 2+\omega +\omega$.

"$\omega \omega +2+\omega 2+\omega 2$, $\omega \omega +2+\omega 2+\omega 2+1$, $\omega \omega +2+\omega 2+\omega 2+2$, $\omega \omega +2+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 2+\omega 2+\omega$.

"$\omega \omega +2+\omega 2+\omega 3$, $\omega \omega +2+\omega 2+\omega 3+1$, $\omega \omega +2+\omega 2+\omega 3+2$, $\omega \omega +2+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 2+\omega 2$.

"$\omega \omega +2+\omega 22$, $\omega \omega +2+\omega 22+1$, $\omega \omega +2+\omega 22+2$, $\omega \omega +2+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 22+\omega$.

"$\omega \omega +2+\omega 22+\omega$, $\omega \omega +2+\omega 22+\omega +1$, $\omega \omega +2+\omega 22+\omega +2$, $\omega \omega +2+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 22+\omega +\omega$.

"$\omega \omega +2+\omega 22+\omega 2$, $\omega \omega +2+\omega 22+\omega 2+1$, $\omega \omega +2+\omega 22+\omega 2+2$, $\omega \omega +2+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 22+\omega 2+\omega$.

"$\omega \omega +2+\omega 22+\omega 3$, $\omega \omega +2+\omega 22+\omega 3+1$, $\omega \omega +2+\omega 22+\omega 3+2$, $\omega \omega +2+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 22+\omega 2$.

"$\omega \omega +2+\omega 23$, $\omega \omega +2+\omega 23+1$, $\omega \omega +2+\omega 23+2$, $\omega \omega +2+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 23+\omega$.

"$\omega \omega +2+\omega 23+\omega$, $\omega \omega +2+\omega 23+\omega +1$, $\omega \omega +2+\omega 23+\omega +2$, $\omega \omega +2+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 23+\omega +\omega$.

"$\omega \omega +2+\omega 23+\omega 2$, $\omega \omega +2+\omega 23+\omega 2+1$, $\omega \omega +2+\omega 23+\omega 2+2$, $\omega \omega +2+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 23+\omega 2+\omega$.

"$\omega \omega +2+\omega 23+\omega 3$, $\omega \omega +2+\omega 23+\omega 3+1$, $\omega \omega +2+\omega 23+\omega 3+2$, $\omega \omega +2+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3$.

"$\omega \omega +2+\omega 3$, $\omega \omega +2+\omega 3+1$, $\omega \omega +2+\omega 3+2$, $\omega \omega +2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega$.

"$\omega \omega +2+\omega 3+\omega$, $\omega \omega +2+\omega 3+\omega +1$, $\omega \omega +2+\omega 3+\omega +2$, $\omega \omega +2+\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega +\omega$.

"$\omega \omega +2+\omega 3+\omega 2$, $\omega \omega +2+\omega 3+\omega 2+1$, $\omega \omega +2+\omega 3+\omega 2+2$, $\omega \omega +2+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 2+\omega$.

"$\omega \omega +2+\omega 3+\omega 3$, $\omega \omega +2+\omega 3+\omega 3+1$, $\omega \omega +2+\omega 3+\omega 3+2$, $\omega \omega +2+\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 2$.

"$\omega \omega +2+\omega 3+\omega 2$, $\omega \omega +2+\omega 3+\omega 2+1$, $\omega \omega +2+\omega 3+\omega 2+2$, $\omega \omega +2+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 2+\omega$.

"$\omega \omega +2+\omega 3+\omega 2+\omega$, $\omega \omega +2+\omega 3+\omega 2+\omega +1$, $\omega \omega +2+\omega 3+\omega 2+\omega +2$, $\omega \omega +2+\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega +2+\omega 3+\omega 2+\omega 2$, $\omega \omega +2+\omega 3+\omega 2+\omega 2+1$, $\omega \omega +2+\omega 3+\omega 2+\omega 2+2$, $\omega \omega +2+\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega +2+\omega 3+\omega 2+\omega 3$, $\omega \omega +2+\omega 3+\omega 2+\omega 3+1$, $\omega \omega +2+\omega 3+\omega 2+\omega 3+2$, $\omega \omega +2+\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 2+\omega 2$.

"$\omega \omega +2+\omega 3+\omega 22$, $\omega \omega +2+\omega 3+\omega 22+1$, $\omega \omega +2+\omega 3+\omega 22+2$, $\omega \omega +2+\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 22+\omega$.

"$\omega \omega +2+\omega 3+\omega 22+\omega$, $\omega \omega +2+\omega 3+\omega 22+\omega +1$, $\omega \omega +2+\omega 3+\omega 22+\omega +2$, $\omega \omega +2+\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega +2+\omega 3+\omega 22+\omega 2$, $\omega \omega +2+\omega 3+\omega 22+\omega 2+1$, $\omega \omega +2+\omega 3+\omega 22+\omega 2+2$, $\omega \omega +2+\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega +2+\omega 3+\omega 22+\omega 3$, $\omega \omega +2+\omega 3+\omega 22+\omega 3+1$, $\omega \omega +2+\omega 3+\omega 22+\omega 3+2$, $\omega \omega +2+\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 22+\omega 2$.

"$\omega \omega +2+\omega 3+\omega 23$, $\omega \omega +2+\omega 3+\omega 23+1$, $\omega \omega +2+\omega 3+\omega 23+2$, $\omega \omega +2+\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 23+\omega$.

"$\omega \omega +2+\omega 3+\omega 23+\omega$, $\omega \omega +2+\omega 3+\omega 23+\omega +1$, $\omega \omega +2+\omega 3+\omega 23+\omega +2$, $\omega \omega +2+\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega +2+\omega 3+\omega 23+\omega 2$, $\omega \omega +2+\omega 3+\omega 23+\omega 2+1$, $\omega \omega +2+\omega 3+\omega 23+\omega 2+2$, $\omega \omega +2+\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega +2+\omega 3+\omega 23+\omega 3$, $\omega \omega +2+\omega 3+\omega 23+\omega 3+1$, $\omega \omega +2+\omega 3+\omega 23+\omega 3+2$, $\omega \omega +2+\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 3+\omega 3$.

"$\omega \omega +2+\omega 32$, $\omega \omega +2+\omega 32+1$, $\omega \omega +2+\omega 32+2$, $\omega \omega +2+\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega$.

"$\omega \omega +2+\omega 32+\omega$, $\omega \omega +2+\omega 32+\omega +1$, $\omega \omega +2+\omega 32+\omega +2$, $\omega \omega +2+\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega +\omega$.

"$\omega \omega +2+\omega 32+\omega 2$, $\omega \omega +2+\omega 32+\omega 2+1$, $\omega \omega +2+\omega 32+\omega 2+2$, $\omega \omega +2+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 2+\omega$.

"$\omega \omega +2+\omega 32+\omega 3$, $\omega \omega +2+\omega 32+\omega 3+1$, $\omega \omega +2+\omega 32+\omega 3+2$, $\omega \omega +2+\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 2$.

"$\omega \omega +2+\omega 32+\omega 2$, $\omega \omega +2+\omega 32+\omega 2+1$, $\omega \omega +2+\omega 32+\omega 2+2$, $\omega \omega +2+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 2+\omega$.

"$\omega \omega +2+\omega 32+\omega 2+\omega$, $\omega \omega +2+\omega 32+\omega 2+\omega +1$, $\omega \omega +2+\omega 32+\omega 2+\omega +2$, $\omega \omega +2+\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega +2+\omega 32+\omega 2+\omega 2$, $\omega \omega +2+\omega 32+\omega 2+\omega 2+1$, $\omega \omega +2+\omega 32+\omega 2+\omega 2+2$, $\omega \omega +2+\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega +2+\omega 32+\omega 2+\omega 3$, $\omega \omega +2+\omega 32+\omega 2+\omega 3+1$, $\omega \omega +2+\omega 32+\omega 2+\omega 3+2$, $\omega \omega +2+\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 2+\omega 2$.

"$\omega \omega +2+\omega 32+\omega 22$, $\omega \omega +2+\omega 32+\omega 22+1$, $\omega \omega +2+\omega 32+\omega 22+2$, $\omega \omega +2+\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 22+\omega$.

"$\omega \omega +2+\omega 32+\omega 22+\omega$, $\omega \omega +2+\omega 32+\omega 22+\omega +1$, $\omega \omega +2+\omega 32+\omega 22+\omega +2$, $\omega \omega +2+\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega +2+\omega 32+\omega 22+\omega 2$, $\omega \omega +2+\omega 32+\omega 22+\omega 2+1$, $\omega \omega +2+\omega 32+\omega 22+\omega 2+2$, $\omega \omega +2+\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega +2+\omega 32+\omega 22+\omega 3$, $\omega \omega +2+\omega 32+\omega 22+\omega 3+1$, $\omega \omega +2+\omega 32+\omega 22+\omega 3+2$, $\omega \omega +2+\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 22+\omega 2$.

"$\omega \omega +2+\omega 32+\omega 23$, $\omega \omega +2+\omega 32+\omega 23+1$, $\omega \omega +2+\omega 32+\omega 23+2$, $\omega \omega +2+\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 23+\omega$.

"$\omega \omega +2+\omega 32+\omega 23+\omega$, $\omega \omega +2+\omega 32+\omega 23+\omega +1$, $\omega \omega +2+\omega 32+\omega 23+\omega +2$, $\omega \omega +2+\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega +2+\omega 32+\omega 23+\omega 2$, $\omega \omega +2+\omega 32+\omega 23+\omega 2+1$, $\omega \omega +2+\omega 32+\omega 23+\omega 2+2$, $\omega \omega +2+\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega +2+\omega 32+\omega 23+\omega 3$, $\omega \omega +2+\omega 32+\omega 23+\omega 3+1$, $\omega \omega +2+\omega 32+\omega 23+\omega 3+2$, $\omega \omega +2+\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 32+\omega 3$.

"$\omega \omega +2+\omega 33$, $\omega \omega +2+\omega 33+1$, $\omega \omega +2+\omega 33+2$, $\omega \omega +2+\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega$.

"$\omega \omega +2+\omega 33+\omega$, $\omega \omega +2+\omega 33+\omega +1$, $\omega \omega +2+\omega 33+\omega +2$, $\omega \omega +2+\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega +\omega$.

"$\omega \omega +2+\omega 33+\omega 2$, $\omega \omega +2+\omega 33+\omega 2+1$, $\omega \omega +2+\omega 33+\omega 2+2$, $\omega \omega +2+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 2+\omega$.

"$\omega \omega +2+\omega 33+\omega 3$, $\omega \omega +2+\omega 33+\omega 3+1$, $\omega \omega +2+\omega 33+\omega 3+2$, $\omega \omega +2+\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 2$.

"$\omega \omega +2+\omega 33+\omega 2$, $\omega \omega +2+\omega 33+\omega 2+1$, $\omega \omega +2+\omega 33+\omega 2+2$, $\omega \omega +2+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 2+\omega$.

"$\omega \omega +2+\omega 33+\omega 2+\omega$, $\omega \omega +2+\omega 33+\omega 2+\omega +1$, $\omega \omega +2+\omega 33+\omega 2+\omega +2$, $\omega \omega +2+\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega +2+\omega 33+\omega 2+\omega 2$, $\omega \omega +2+\omega 33+\omega 2+\omega 2+1$, $\omega \omega +2+\omega 33+\omega 2+\omega 2+2$, $\omega \omega +2+\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega +2+\omega 33+\omega 2+\omega 3$, $\omega \omega +2+\omega 33+\omega 2+\omega 3+1$, $\omega \omega +2+\omega 33+\omega 2+\omega 3+2$, $\omega \omega +2+\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 2+\omega 2$.

"$\omega \omega +2+\omega 33+\omega 22$, $\omega \omega +2+\omega 33+\omega 22+1$, $\omega \omega +2+\omega 33+\omega 22+2$, $\omega \omega +2+\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 22+\omega$.

"$\omega \omega +2+\omega 33+\omega 22+\omega$, $\omega \omega +2+\omega 33+\omega 22+\omega +1$, $\omega \omega +2+\omega 33+\omega 22+\omega +2$, $\omega \omega +2+\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega +2+\omega 33+\omega 22+\omega 2$, $\omega \omega +2+\omega 33+\omega 22+\omega 2+1$, $\omega \omega +2+\omega 33+\omega 22+\omega 2+2$, $\omega \omega +2+\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega +2+\omega 33+\omega 22+\omega 3$, $\omega \omega +2+\omega 33+\omega 22+\omega 3+1$, $\omega \omega +2+\omega 33+\omega 22+\omega 3+2$, $\omega \omega +2+\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 22+\omega 2$.

"$\omega \omega +2+\omega 33+\omega 23$, $\omega \omega +2+\omega 33+\omega 23+1$, $\omega \omega +2+\omega 33+\omega 23+2$, $\omega \omega +2+\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 23+\omega$.

"$\omega \omega +2+\omega 33+\omega 23+\omega$, $\omega \omega +2+\omega 33+\omega 23+\omega +1$, $\omega \omega +2+\omega 33+\omega 23+\omega +2$, $\omega \omega +2+\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega +2+\omega 33+\omega 23+\omega 2$, $\omega \omega +2+\omega 33+\omega 23+\omega 2+1$, $\omega \omega +2+\omega 33+\omega 23+\omega 2+2$, $\omega \omega +2+\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega +2+\omega 33+\omega 23+\omega 3$, $\omega \omega +2+\omega 33+\omega 23+\omega 3+1$, $\omega \omega +2+\omega 33+\omega 23+\omega 3+2$, $\omega \omega +2+\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +2+\omega 33+\omega 3$.

"$\omega \omega +22$, $\omega \omega +22+1$, $\omega \omega +22+2$, $\omega \omega +22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega$.

"$\omega \omega +22+\omega$, $\omega \omega +22+\omega +1$, $\omega \omega +22+\omega +2$, $\omega \omega +22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega +\omega$.

"$\omega \omega +22+\omega 2$, $\omega \omega +22+\omega 2+1$, $\omega \omega +22+\omega 2+2$, $\omega \omega +22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 2+\omega$.

"$\omega \omega +22+\omega 3$, $\omega \omega +22+\omega 3+1$, $\omega \omega +22+\omega 3+2$, $\omega \omega +22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 2$.

"$\omega \omega +22+\omega 2$, $\omega \omega +22+\omega 2+1$, $\omega \omega +22+\omega 2+2$, $\omega \omega +22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 2+\omega$.

"$\omega \omega +22+\omega 2+\omega$, $\omega \omega +22+\omega 2+\omega +1$, $\omega \omega +22+\omega 2+\omega +2$, $\omega \omega +22+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 2+\omega +\omega$.

"$\omega \omega +22+\omega 2+\omega 2$, $\omega \omega +22+\omega 2+\omega 2+1$, $\omega \omega +22+\omega 2+\omega 2+2$, $\omega \omega +22+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 2+\omega 2+\omega$.

"$\omega \omega +22+\omega 2+\omega 3$, $\omega \omega +22+\omega 2+\omega 3+1$, $\omega \omega +22+\omega 2+\omega 3+2$, $\omega \omega +22+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 2+\omega 2$.

"$\omega \omega +22+\omega 22$, $\omega \omega +22+\omega 22+1$, $\omega \omega +22+\omega 22+2$, $\omega \omega +22+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 22+\omega$.

"$\omega \omega +22+\omega 22+\omega$, $\omega \omega +22+\omega 22+\omega +1$, $\omega \omega +22+\omega 22+\omega +2$, $\omega \omega +22+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 22+\omega +\omega$.

"$\omega \omega +22+\omega 22+\omega 2$, $\omega \omega +22+\omega 22+\omega 2+1$, $\omega \omega +22+\omega 22+\omega 2+2$, $\omega \omega +22+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 22+\omega 2+\omega$.

"$\omega \omega +22+\omega 22+\omega 3$, $\omega \omega +22+\omega 22+\omega 3+1$, $\omega \omega +22+\omega 22+\omega 3+2$, $\omega \omega +22+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 22+\omega 2$.

"$\omega \omega +22+\omega 23$, $\omega \omega +22+\omega 23+1$, $\omega \omega +22+\omega 23+2$, $\omega \omega +22+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 23+\omega$.

"$\omega \omega +22+\omega 23+\omega$, $\omega \omega +22+\omega 23+\omega +1$, $\omega \omega +22+\omega 23+\omega +2$, $\omega \omega +22+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 23+\omega +\omega$.

"$\omega \omega +22+\omega 23+\omega 2$, $\omega \omega +22+\omega 23+\omega 2+1$, $\omega \omega +22+\omega 23+\omega 2+2$, $\omega \omega +22+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 23+\omega 2+\omega$.

"$\omega \omega +22+\omega 23+\omega 3$, $\omega \omega +22+\omega 23+\omega 3+1$, $\omega \omega +22+\omega 23+\omega 3+2$, $\omega \omega +22+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3$.

"$\omega \omega +22+\omega 3$, $\omega \omega +22+\omega 3+1$, $\omega \omega +22+\omega 3+2$, $\omega \omega +22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega$.

"$\omega \omega +22+\omega 3+\omega$, $\omega \omega +22+\omega 3+\omega +1$, $\omega \omega +22+\omega 3+\omega +2$, $\omega \omega +22+\omega 3+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega +\omega$.

"$\omega \omega +22+\omega 3+\omega 2$, $\omega \omega +22+\omega 3+\omega 2+1$, $\omega \omega +22+\omega 3+\omega 2+2$, $\omega \omega +22+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 2+\omega$.

"$\omega \omega +22+\omega 3+\omega 3$, $\omega \omega +22+\omega 3+\omega 3+1$, $\omega \omega +22+\omega 3+\omega 3+2$, $\omega \omega +22+\omega 3+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 2$.

"$\omega \omega +22+\omega 3+\omega 2$, $\omega \omega +22+\omega 3+\omega 2+1$, $\omega \omega +22+\omega 3+\omega 2+2$, $\omega \omega +22+\omega 3+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 2+\omega$.

"$\omega \omega +22+\omega 3+\omega 2+\omega$, $\omega \omega +22+\omega 3+\omega 2+\omega +1$, $\omega \omega +22+\omega 3+\omega 2+\omega +2$, $\omega \omega +22+\omega 3+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 2+\omega +\omega$.

"$\omega \omega +22+\omega 3+\omega 2+\omega 2$, $\omega \omega +22+\omega 3+\omega 2+\omega 2+1$, $\omega \omega +22+\omega 3+\omega 2+\omega 2+2$, $\omega \omega +22+\omega 3+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 2+\omega 2+\omega$.

"$\omega \omega +22+\omega 3+\omega 2+\omega 3$, $\omega \omega +22+\omega 3+\omega 2+\omega 3+1$, $\omega \omega +22+\omega 3+\omega 2+\omega 3+2$, $\omega \omega +22+\omega 3+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 2+\omega 2$.

"$\omega \omega +22+\omega 3+\omega 22$, $\omega \omega +22+\omega 3+\omega 22+1$, $\omega \omega +22+\omega 3+\omega 22+2$, $\omega \omega +22+\omega 3+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 22+\omega$.

"$\omega \omega +22+\omega 3+\omega 22+\omega$, $\omega \omega +22+\omega 3+\omega 22+\omega +1$, $\omega \omega +22+\omega 3+\omega 22+\omega +2$, $\omega \omega +22+\omega 3+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 22+\omega +\omega$.

"$\omega \omega +22+\omega 3+\omega 22+\omega 2$, $\omega \omega +22+\omega 3+\omega 22+\omega 2+1$, $\omega \omega +22+\omega 3+\omega 22+\omega 2+2$, $\omega \omega +22+\omega 3+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 22+\omega 2+\omega$.

"$\omega \omega +22+\omega 3+\omega 22+\omega 3$, $\omega \omega +22+\omega 3+\omega 22+\omega 3+1$, $\omega \omega +22+\omega 3+\omega 22+\omega 3+2$, $\omega \omega +22+\omega 3+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 22+\omega 2$.

"$\omega \omega +22+\omega 3+\omega 23$, $\omega \omega +22+\omega 3+\omega 23+1$, $\omega \omega +22+\omega 3+\omega 23+2$, $\omega \omega +22+\omega 3+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 23+\omega$.

"$\omega \omega +22+\omega 3+\omega 23+\omega$, $\omega \omega +22+\omega 3+\omega 23+\omega +1$, $\omega \omega +22+\omega 3+\omega 23+\omega +2$, $\omega \omega +22+\omega 3+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 23+\omega +\omega$.

"$\omega \omega +22+\omega 3+\omega 23+\omega 2$, $\omega \omega +22+\omega 3+\omega 23+\omega 2+1$, $\omega \omega +22+\omega 3+\omega 23+\omega 2+2$, $\omega \omega +22+\omega 3+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 23+\omega 2+\omega$.

"$\omega \omega +22+\omega 3+\omega 23+\omega 3$, $\omega \omega +22+\omega 3+\omega 23+\omega 3+1$, $\omega \omega +22+\omega 3+\omega 23+\omega 3+2$, $\omega \omega +22+\omega 3+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 3+\omega 3$.

"$\omega \omega +22+\omega 32$, $\omega \omega +22+\omega 32+1$, $\omega \omega +22+\omega 32+2$, $\omega \omega +22+\omega 32+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega$.

"$\omega \omega +22+\omega 32+\omega$, $\omega \omega +22+\omega 32+\omega +1$, $\omega \omega +22+\omega 32+\omega +2$, $\omega \omega +22+\omega 32+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega +\omega$.

"$\omega \omega +22+\omega 32+\omega 2$, $\omega \omega +22+\omega 32+\omega 2+1$, $\omega \omega +22+\omega 32+\omega 2+2$, $\omega \omega +22+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 2+\omega$.

"$\omega \omega +22+\omega 32+\omega 3$, $\omega \omega +22+\omega 32+\omega 3+1$, $\omega \omega +22+\omega 32+\omega 3+2$, $\omega \omega +22+\omega 32+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 2$.

"$\omega \omega +22+\omega 32+\omega 2$, $\omega \omega +22+\omega 32+\omega 2+1$, $\omega \omega +22+\omega 32+\omega 2+2$, $\omega \omega +22+\omega 32+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 2+\omega$.

"$\omega \omega +22+\omega 32+\omega 2+\omega$, $\omega \omega +22+\omega 32+\omega 2+\omega +1$, $\omega \omega +22+\omega 32+\omega 2+\omega +2$, $\omega \omega +22+\omega 32+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 2+\omega +\omega$.

"$\omega \omega +22+\omega 32+\omega 2+\omega 2$, $\omega \omega +22+\omega 32+\omega 2+\omega 2+1$, $\omega \omega +22+\omega 32+\omega 2+\omega 2+2$, $\omega \omega +22+\omega 32+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 2+\omega 2+\omega$.

"$\omega \omega +22+\omega 32+\omega 2+\omega 3$, $\omega \omega +22+\omega 32+\omega 2+\omega 3+1$, $\omega \omega +22+\omega 32+\omega 2+\omega 3+2$, $\omega \omega +22+\omega 32+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 2+\omega 2$.

"$\omega \omega +22+\omega 32+\omega 22$, $\omega \omega +22+\omega 32+\omega 22+1$, $\omega \omega +22+\omega 32+\omega 22+2$, $\omega \omega +22+\omega 32+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 22+\omega$.

"$\omega \omega +22+\omega 32+\omega 22+\omega$, $\omega \omega +22+\omega 32+\omega 22+\omega +1$, $\omega \omega +22+\omega 32+\omega 22+\omega +2$, $\omega \omega +22+\omega 32+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 22+\omega +\omega$.

"$\omega \omega +22+\omega 32+\omega 22+\omega 2$, $\omega \omega +22+\omega 32+\omega 22+\omega 2+1$, $\omega \omega +22+\omega 32+\omega 22+\omega 2+2$, $\omega \omega +22+\omega 32+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 22+\omega 2+\omega$.

"$\omega \omega +22+\omega 32+\omega 22+\omega 3$, $\omega \omega +22+\omega 32+\omega 22+\omega 3+1$, $\omega \omega +22+\omega 32+\omega 22+\omega 3+2$, $\omega \omega +22+\omega 32+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 22+\omega 2$.

"$\omega \omega +22+\omega 32+\omega 23$, $\omega \omega +22+\omega 32+\omega 23+1$, $\omega \omega +22+\omega 32+\omega 23+2$, $\omega \omega +22+\omega 32+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 23+\omega$.

"$\omega \omega +22+\omega 32+\omega 23+\omega$, $\omega \omega +22+\omega 32+\omega 23+\omega +1$, $\omega \omega +22+\omega 32+\omega 23+\omega +2$, $\omega \omega +22+\omega 32+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 23+\omega +\omega$.

"$\omega \omega +22+\omega 32+\omega 23+\omega 2$, $\omega \omega +22+\omega 32+\omega 23+\omega 2+1$, $\omega \omega +22+\omega 32+\omega 23+\omega 2+2$, $\omega \omega +22+\omega 32+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 23+\omega 2+\omega$.

"$\omega \omega +22+\omega 32+\omega 23+\omega 3$, $\omega \omega +22+\omega 32+\omega 23+\omega 3+1$, $\omega \omega +22+\omega 32+\omega 23+\omega 3+2$, $\omega \omega +22+\omega 32+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 32+\omega 3$.

"$\omega \omega +22+\omega 33$, $\omega \omega +22+\omega 33+1$, $\omega \omega +22+\omega 33+2$, $\omega \omega +22+\omega 33+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega$.

"$\omega \omega +22+\omega 33+\omega$, $\omega \omega +22+\omega 33+\omega +1$, $\omega \omega +22+\omega 33+\omega +2$, $\omega \omega +22+\omega 33+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega +\omega$.

"$\omega \omega +22+\omega 33+\omega 2$, $\omega \omega +22+\omega 33+\omega 2+1$, $\omega \omega +22+\omega 33+\omega 2+2$, $\omega \omega +22+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 2+\omega$.

"$\omega \omega +22+\omega 33+\omega 3$, $\omega \omega +22+\omega 33+\omega 3+1$, $\omega \omega +22+\omega 33+\omega 3+2$, $\omega \omega +22+\omega 33+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 2$.

"$\omega \omega +22+\omega 33+\omega 2$, $\omega \omega +22+\omega 33+\omega 2+1$, $\omega \omega +22+\omega 33+\omega 2+2$, $\omega \omega +22+\omega 33+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 2+\omega$.

"$\omega \omega +22+\omega 33+\omega 2+\omega$, $\omega \omega +22+\omega 33+\omega 2+\omega +1$, $\omega \omega +22+\omega 33+\omega 2+\omega +2$, $\omega \omega +22+\omega 33+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 2+\omega +\omega$.

"$\omega \omega +22+\omega 33+\omega 2+\omega 2$, $\omega \omega +22+\omega 33+\omega 2+\omega 2+1$, $\omega \omega +22+\omega 33+\omega 2+\omega 2+2$, $\omega \omega +22+\omega 33+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 2+\omega 2+\omega$.

"$\omega \omega +22+\omega 33+\omega 2+\omega 3$, $\omega \omega +22+\omega 33+\omega 2+\omega 3+1$, $\omega \omega +22+\omega 33+\omega 2+\omega 3+2$, $\omega \omega +22+\omega 33+\omega 2+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 2+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 2+\omega 2$.

"$\omega \omega +22+\omega 33+\omega 22$, $\omega \omega +22+\omega 33+\omega 22+1$, $\omega \omega +22+\omega 33+\omega 22+2$, $\omega \omega +22+\omega 33+\omega 22+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 22+\omega$.

"$\omega \omega +22+\omega 33+\omega 22+\omega$, $\omega \omega +22+\omega 33+\omega 22+\omega +1$, $\omega \omega +22+\omega 33+\omega 22+\omega +2$, $\omega \omega +22+\omega 33+\omega 22+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 22+\omega +\omega$.

"$\omega \omega +22+\omega 33+\omega 22+\omega 2$, $\omega \omega +22+\omega 33+\omega 22+\omega 2+1$, $\omega \omega +22+\omega 33+\omega 22+\omega 2+2$, $\omega \omega +22+\omega 33+\omega 22+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 22+\omega 2+\omega$.

"$\omega \omega +22+\omega 33+\omega 22+\omega 3$, $\omega \omega +22+\omega 33+\omega 22+\omega 3+1$, $\omega \omega +22+\omega 33+\omega 22+\omega 3+2$, $\omega \omega +22+\omega 33+\omega 22+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 22+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 22+\omega 2$.

"$\omega \omega +22+\omega 33+\omega 23$, $\omega \omega +22+\omega 33+\omega 23+1$, $\omega \omega +22+\omega 33+\omega 23+2$, $\omega \omega +22+\omega 33+\omega 23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 23+\omega$.

"$\omega \omega +22+\omega 33+\omega 23+\omega$, $\omega \omega +22+\omega 33+\omega 23+\omega +1$, $\omega \omega +22+\omega 33+\omega 23+\omega +2$, $\omega \omega +22+\omega 33+\omega 23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 23+\omega +\omega$.

"$\omega \omega +22+\omega 33+\omega 23+\omega 2$, $\omega \omega +22+\omega 33+\omega 23+\omega 2+1$, $\omega \omega +22+\omega 33+\omega 23+\omega 2+2$, $\omega \omega +22+\omega 33+\omega 23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 23+\omega 2+\omega$.

"$\omega \omega +22+\omega 33+\omega 23+\omega 3$, $\omega \omega +22+\omega 33+\omega 23+\omega 3+1$, $\omega \omega +22+\omega 33+\omega 23+\omega 3+2$, $\omega \omega +22+\omega 33+\omega 23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 23+\omega 2$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +22+\omega 33+\omega 3$.

"$\omega \omega +23$, $\omega \omega +23+1$, $\omega \omega +23+2$, $\omega \omega +23+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega$.

"$\omega \omega +23+\omega$, $\omega \omega +23+\omega +1$, $\omega \omega +23+\omega +2$, $\omega \omega +23+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega +\omega$.

"$\omega \omega +23+\omega 2$, $\omega \omega +23+\omega 2+1$, $\omega \omega +23+\omega 2+2$, $\omega \omega +23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega 2+\omega$.

"$\omega \omega +23+\omega 3$, $\omega \omega +23+\omega 3+1$, $\omega \omega +23+\omega 3+2$, $\omega \omega +23+\omega 3+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega 3+\omega$.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega 2$.

"$\omega \omega +23+\omega 2$, $\omega \omega +23+\omega 2+1$, $\omega \omega +23+\omega 2+2$, $\omega \omega +23+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega 2+\omega$.

"$\omega \omega +23+\omega 2+\omega$, $\omega \omega +23+\omega 2+\omega +1$, $\omega \omega +23+\omega 2+\omega +2$, $\omega \omega +23+\omega 2+\omega +3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega 2+\omega +\omega$.

"$\omega \omega +23+\omega 2+\omega 2$, $\omega \omega +23+\omega 2+\omega 2+1$, $\omega \omega +23+\omega 2+\omega 2+2$, $\omega \omega +23+\omega 2+\omega 2+3$, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $\omega \omega +23+\omega 2+\omega 2+\omega$.

"$\omega \omega +23+\omega 2+\omega 3$, $\omega \omega +23+\omega 2+\omega 3+1$, $<$