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.

" $ω$ , $ω + 1$ , $ω + 2$ , $ω + 3$ , ... ".

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

" $ω 2$ , $ω 2 + 1$ , $ω 2 + 2$ , $ω 2 + 3$ , ... ".

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

" $ω 3$ , $ω 3 + 1$ , $ω 3 + 2$ , $ω 3 + 3$ , ... ".

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

...

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

" $ω$ ², $ω$ ² + 1, $ω$ ² + 2, $ω$ ² + 3, ... ".

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

" $ω$ ² + ω, $ω$ ² + ω + 1, $ω$ ² + ω + 2, $ω$ ² + ω + 3, ... ".

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

" $ω$ ² + ω⁢2, $ω$ ² + ω⁢2 + 1, $ω$ ² + ω⁢2 + 2, $ω$ ² + ω⁢2 + 3, ... ".

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

" $ω$ ² + ω⁢3, $ω$ ² + ω⁢3 + 1, $ω$ ² + ω⁢3 + 2, $ω$ ² + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ² + ω².

" $ω$ ²⁢2, $ω$ ²⁢2 + 1, $ω$ ²⁢2 + 2, $ω$ ²⁢2 + 3, ... ".

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

" $ω$ ²⁢2 + ω, $ω$ ²⁢2 + ω + 1, $ω$ ²⁢2 + ω + 2, $ω$ ²⁢2 + ω + 3, ... ".

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

" $ω$ ²⁢2 + ω⁢2, $ω$ ²⁢2 + ω⁢2 + 1, $ω$ ²⁢2 + ω⁢2 + 2, $ω$ ²⁢2 + ω⁢2 + 3, ... ".

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

" $ω$ ²⁢2 + ω⁢3, $ω$ ²⁢2 + ω⁢3 + 1, $ω$ ²⁢2 + ω⁢3 + 2, $ω$ ²⁢2 + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ²⁢2 + ω².

" $ω$ ²⁢3, $ω$ ²⁢3 + 1, $ω$ ²⁢3 + 2, $ω$ ²⁢3 + 3, ... ".

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

" $ω$ ²⁢3 + ω, $ω$ ²⁢3 + ω + 1, $ω$ ²⁢3 + ω + 2, $ω$ ²⁢3 + ω + 3, ... ".

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

" $ω$ ²⁢3 + ω⁢2, $ω$ ²⁢3 + ω⁢2 + 1, $ω$ ²⁢3 + ω⁢2 + 2, $ω$ ²⁢3 + ω⁢2 + 3, ... ".

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

" $ω$ ²⁢3 + ω⁢3, $ω$ ²⁢3 + ω⁢3 + 1, $ω$ ²⁢3 + ω⁢3 + 2, $ω$ ²⁢3 + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ²⁢3 + ω².

...

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

" $ω$ ³, $ω$ ³ + 1, $ω$ ³ + 2, $ω$ ³ + 3, ... ".

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

" $ω$ ³ + ω, $ω$ ³ + ω + 1, $ω$ ³ + ω + 2, $ω$ ³ + ω + 3, ... ".

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

" $ω$ ³ + ω⁢2, $ω$ ³ + ω⁢2 + 1, $ω$ ³ + ω⁢2 + 2, $ω$ ³ + ω⁢2 + 3, ... ".

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

" $ω$ ³ + ω⁢3, $ω$ ³ + ω⁢3 + 1, $ω$ ³ + ω⁢3 + 2, $ω$ ³ + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω².

" $ω$ ³ + ω², $ω$ ³ + ω² + 1, $ω$ ³ + ω² + 2, $ω$ ³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω² + ω.

" $ω$ ³ + ω² + ω, $ω$ ³ + ω² + ω + 1, $ω$ ³ + ω² + ω + 2, $ω$ ³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω² + ω + ω.

" $ω$ ³ + ω² + ω⁢2, $ω$ ³ + ω² + ω⁢2 + 1, $ω$ ³ + ω² + ω⁢2 + 2, $ω$ ³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω² + ω⁢2 + ω.

" $ω$ ³ + ω² + ω⁢3, $ω$ ³ + ω² + ω⁢3 + 1, $ω$ ³ + ω² + ω⁢3 + 2, $ω$ ³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω² + ω².

" $ω$ ³ + ω²⁢2, $ω$ ³ + ω²⁢2 + 1, $ω$ ³ + ω²⁢2 + 2, $ω$ ³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢2 + ω.

" $ω$ ³ + ω²⁢2 + ω, $ω$ ³ + ω²⁢2 + ω + 1, $ω$ ³ + ω²⁢2 + ω + 2, $ω$ ³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢2 + ω + ω.

" $ω$ ³ + ω²⁢2 + ω⁢2, $ω$ ³ + ω²⁢2 + ω⁢2 + 1, $ω$ ³ + ω²⁢2 + ω⁢2 + 2, $ω$ ³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ³ + ω²⁢2 + ω⁢3, $ω$ ³ + ω²⁢2 + ω⁢3 + 1, $ω$ ³ + ω²⁢2 + ω⁢3 + 2, $ω$ ³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢2 + ω².

" $ω$ ³ + ω²⁢3, $ω$ ³ + ω²⁢3 + 1, $ω$ ³ + ω²⁢3 + 2, $ω$ ³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢3 + ω.

" $ω$ ³ + ω²⁢3 + ω, $ω$ ³ + ω²⁢3 + ω + 1, $ω$ ³ + ω²⁢3 + ω + 2, $ω$ ³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢3 + ω + ω.

" $ω$ ³ + ω²⁢3 + ω⁢2, $ω$ ³ + ω²⁢3 + ω⁢2 + 1, $ω$ ³ + ω²⁢3 + ω⁢2 + 2, $ω$ ³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ³ + ω²⁢3 + ω⁢3, $ω$ ³ + ω²⁢3 + ω⁢3 + 1, $ω$ ³ + ω²⁢3 + ω⁢3 + 2, $ω$ ³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³ + ω³.

" $ω$ ³⁢2, $ω$ ³⁢2 + 1, $ω$ ³⁢2 + 2, $ω$ ³⁢2 + 3, ... ".

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

" $ω$ ³⁢2 + ω, $ω$ ³⁢2 + ω + 1, $ω$ ³⁢2 + ω + 2, $ω$ ³⁢2 + ω + 3, ... ".

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

" $ω$ ³⁢2 + ω⁢2, $ω$ ³⁢2 + ω⁢2 + 1, $ω$ ³⁢2 + ω⁢2 + 2, $ω$ ³⁢2 + ω⁢2 + 3, ... ".

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

" $ω$ ³⁢2 + ω⁢3, $ω$ ³⁢2 + ω⁢3 + 1, $ω$ ³⁢2 + ω⁢3 + 2, $ω$ ³⁢2 + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω².

" $ω$ ³⁢2 + ω², $ω$ ³⁢2 + ω² + 1, $ω$ ³⁢2 + ω² + 2, $ω$ ³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω² + ω.

" $ω$ ³⁢2 + ω² + ω, $ω$ ³⁢2 + ω² + ω + 1, $ω$ ³⁢2 + ω² + ω + 2, $ω$ ³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω² + ω + ω.

" $ω$ ³⁢2 + ω² + ω⁢2, $ω$ ³⁢2 + ω² + ω⁢2 + 1, $ω$ ³⁢2 + ω² + ω⁢2 + 2, $ω$ ³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ³⁢2 + ω² + ω⁢3, $ω$ ³⁢2 + ω² + ω⁢3 + 1, $ω$ ³⁢2 + ω² + ω⁢3 + 2, $ω$ ³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω² + ω².

" $ω$ ³⁢2 + ω²⁢2, $ω$ ³⁢2 + ω²⁢2 + 1, $ω$ ³⁢2 + ω²⁢2 + 2, $ω$ ³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢2 + ω.

" $ω$ ³⁢2 + ω²⁢2 + ω, $ω$ ³⁢2 + ω²⁢2 + ω + 1, $ω$ ³⁢2 + ω²⁢2 + ω + 2, $ω$ ³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ³⁢2 + ω²⁢2 + ω⁢2, $ω$ ³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ³⁢2 + ω²⁢2 + ω⁢3, $ω$ ³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢2 + ω².

" $ω$ ³⁢2 + ω²⁢3, $ω$ ³⁢2 + ω²⁢3 + 1, $ω$ ³⁢2 + ω²⁢3 + 2, $ω$ ³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢3 + ω.

" $ω$ ³⁢2 + ω²⁢3 + ω, $ω$ ³⁢2 + ω²⁢3 + ω + 1, $ω$ ³⁢2 + ω²⁢3 + ω + 2, $ω$ ³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ³⁢2 + ω²⁢3 + ω⁢2, $ω$ ³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ³⁢2 + ω²⁢3 + ω⁢3, $ω$ ³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢2 + ω³.

" $ω$ ³⁢3, $ω$ ³⁢3 + 1, $ω$ ³⁢3 + 2, $ω$ ³⁢3 + 3, ... ".

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

" $ω$ ³⁢3 + ω, $ω$ ³⁢3 + ω + 1, $ω$ ³⁢3 + ω + 2, $ω$ ³⁢3 + ω + 3, ... ".

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

" $ω$ ³⁢3 + ω⁢2, $ω$ ³⁢3 + ω⁢2 + 1, $ω$ ³⁢3 + ω⁢2 + 2, $ω$ ³⁢3 + ω⁢2 + 3, ... ".

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

" $ω$ ³⁢3 + ω⁢3, $ω$ ³⁢3 + ω⁢3 + 1, $ω$ ³⁢3 + ω⁢3 + 2, $ω$ ³⁢3 + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω².

" $ω$ ³⁢3 + ω², $ω$ ³⁢3 + ω² + 1, $ω$ ³⁢3 + ω² + 2, $ω$ ³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω² + ω.

" $ω$ ³⁢3 + ω² + ω, $ω$ ³⁢3 + ω² + ω + 1, $ω$ ³⁢3 + ω² + ω + 2, $ω$ ³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω² + ω + ω.

" $ω$ ³⁢3 + ω² + ω⁢2, $ω$ ³⁢3 + ω² + ω⁢2 + 1, $ω$ ³⁢3 + ω² + ω⁢2 + 2, $ω$ ³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ³⁢3 + ω² + ω⁢3, $ω$ ³⁢3 + ω² + ω⁢3 + 1, $ω$ ³⁢3 + ω² + ω⁢3 + 2, $ω$ ³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω² + ω².

" $ω$ ³⁢3 + ω²⁢2, $ω$ ³⁢3 + ω²⁢2 + 1, $ω$ ³⁢3 + ω²⁢2 + 2, $ω$ ³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢2 + ω.

" $ω$ ³⁢3 + ω²⁢2 + ω, $ω$ ³⁢3 + ω²⁢2 + ω + 1, $ω$ ³⁢3 + ω²⁢2 + ω + 2, $ω$ ³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ³⁢3 + ω²⁢2 + ω⁢2, $ω$ ³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ³⁢3 + ω²⁢2 + ω⁢3, $ω$ ³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢2 + ω².

" $ω$ ³⁢3 + ω²⁢3, $ω$ ³⁢3 + ω²⁢3 + 1, $ω$ ³⁢3 + ω²⁢3 + 2, $ω$ ³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢3 + ω.

" $ω$ ³⁢3 + ω²⁢3 + ω, $ω$ ³⁢3 + ω²⁢3 + ω + 1, $ω$ ³⁢3 + ω²⁢3 + ω + 2, $ω$ ³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ³⁢3 + ω²⁢3 + ω⁢2, $ω$ ³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ³⁢3 + ω²⁢3 + ω⁢3, $ω$ ³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ³⁢3 + ω³.

...

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

" $ω$ ^ω, $ω$ ^ω + 1, $ω$ ^ω + 2, $ω$ ^ω + 3, ... ".

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

" $ω$ ^ω + ω, $ω$ ^ω + ω + 1, $ω$ ^ω + ω + 2, $ω$ ^ω + ω + 3, ... ".

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

" $ω$ ^ω + ω⁢2, $ω$ ^ω + ω⁢2 + 1, $ω$ ^ω + ω⁢2 + 2, $ω$ ^ω + ω⁢2 + 3, ... ".

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

" $ω$ ^ω + ω⁢3, $ω$ ^ω + ω⁢3 + 1, $ω$ ^ω + ω⁢3 + 2, $ω$ ^ω + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω².

" $ω$ ^ω + ω², $ω$ ^ω + ω² + 1, $ω$ ^ω + ω² + 2, $ω$ ^ω + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω² + ω.

" $ω$ ^ω + ω² + ω, $ω$ ^ω + ω² + ω + 1, $ω$ ^ω + ω² + ω + 2, $ω$ ^ω + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω² + ω + ω.

" $ω$ ^ω + ω² + ω⁢2, $ω$ ^ω + ω² + ω⁢2 + 1, $ω$ ^ω + ω² + ω⁢2 + 2, $ω$ ^ω + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω² + ω⁢2 + ω.

" $ω$ ^ω + ω² + ω⁢3, $ω$ ^ω + ω² + ω⁢3 + 1, $ω$ ^ω + ω² + ω⁢3 + 2, $ω$ ^ω + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω² + ω².

" $ω$ ^ω + ω²⁢2, $ω$ ^ω + ω²⁢2 + 1, $ω$ ^ω + ω²⁢2 + 2, $ω$ ^ω + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢2 + ω.

" $ω$ ^ω + ω²⁢2 + ω, $ω$ ^ω + ω²⁢2 + ω + 1, $ω$ ^ω + ω²⁢2 + ω + 2, $ω$ ^ω + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢2 + ω + ω.

" $ω$ ^ω + ω²⁢2 + ω⁢2, $ω$ ^ω + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω + ω²⁢2 + ω⁢3, $ω$ ^ω + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢2 + ω².

" $ω$ ^ω + ω²⁢3, $ω$ ^ω + ω²⁢3 + 1, $ω$ ^ω + ω²⁢3 + 2, $ω$ ^ω + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢3 + ω.

" $ω$ ^ω + ω²⁢3 + ω, $ω$ ^ω + ω²⁢3 + ω + 1, $ω$ ^ω + ω²⁢3 + ω + 2, $ω$ ^ω + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢3 + ω + ω.

" $ω$ ^ω + ω²⁢3 + ω⁢2, $ω$ ^ω + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω + ω²⁢3 + ω⁢3, $ω$ ^ω + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³.

" $ω$ ^ω + ω³, $ω$ ^ω + ω³ + 1, $ω$ ^ω + ω³ + 2, $ω$ ^ω + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω.

" $ω$ ^ω + ω³ + ω, $ω$ ^ω + ω³ + ω + 1, $ω$ ^ω + ω³ + ω + 2, $ω$ ^ω + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω + ω.

" $ω$ ^ω + ω³ + ω⁢2, $ω$ ^ω + ω³ + ω⁢2 + 1, $ω$ ^ω + ω³ + ω⁢2 + 2, $ω$ ^ω + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω⁢2 + ω.

" $ω$ ^ω + ω³ + ω⁢3, $ω$ ^ω + ω³ + ω⁢3 + 1, $ω$ ^ω + ω³ + ω⁢3 + 2, $ω$ ^ω + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω².

" $ω$ ^ω + ω³ + ω², $ω$ ^ω + ω³ + ω² + 1, $ω$ ^ω + ω³ + ω² + 2, $ω$ ^ω + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω² + ω.

" $ω$ ^ω + ω³ + ω² + ω, $ω$ ^ω + ω³ + ω² + ω + 1, $ω$ ^ω + ω³ + ω² + ω + 2, $ω$ ^ω + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω² + ω + ω.

" $ω$ ^ω + ω³ + ω² + ω⁢2, $ω$ ^ω + ω³ + ω² + ω⁢2 + 1, $ω$ ^ω + ω³ + ω² + ω⁢2 + 2, $ω$ ^ω + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^ω + ω³ + ω² + ω⁢3, $ω$ ^ω + ω³ + ω² + ω⁢3 + 1, $ω$ ^ω + ω³ + ω² + ω⁢3 + 2, $ω$ ^ω + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω² + ω².

" $ω$ ^ω + ω³ + ω²⁢2, $ω$ ^ω + ω³ + ω²⁢2 + 1, $ω$ ^ω + ω³ + ω²⁢2 + 2, $ω$ ^ω + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢2 + ω.

" $ω$ ^ω + ω³ + ω²⁢2 + ω, $ω$ ^ω + ω³ + ω²⁢2 + ω + 1, $ω$ ^ω + ω³ + ω²⁢2 + ω + 2, $ω$ ^ω + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^ω + ω³ + ω²⁢2 + ω⁢2, $ω$ ^ω + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω + ω³ + ω²⁢2 + ω⁢3, $ω$ ^ω + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢2 + ω².

" $ω$ ^ω + ω³ + ω²⁢3, $ω$ ^ω + ω³ + ω²⁢3 + 1, $ω$ ^ω + ω³ + ω²⁢3 + 2, $ω$ ^ω + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢3 + ω.

" $ω$ ^ω + ω³ + ω²⁢3 + ω, $ω$ ^ω + ω³ + ω²⁢3 + ω + 1, $ω$ ^ω + ω³ + ω²⁢3 + ω + 2, $ω$ ^ω + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^ω + ω³ + ω²⁢3 + ω⁢2, $ω$ ^ω + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω + ω³ + ω²⁢3 + ω⁢3, $ω$ ^ω + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³ + ω³.

" $ω$ ^ω + ω³⁢2, $ω$ ^ω + ω³⁢2 + 1, $ω$ ^ω + ω³⁢2 + 2, $ω$ ^ω + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω.

" $ω$ ^ω + ω³⁢2 + ω, $ω$ ^ω + ω³⁢2 + ω + 1, $ω$ ^ω + ω³⁢2 + ω + 2, $ω$ ^ω + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω + ω.

" $ω$ ^ω + ω³⁢2 + ω⁢2, $ω$ ^ω + ω³⁢2 + ω⁢2 + 1, $ω$ ^ω + ω³⁢2 + ω⁢2 + 2, $ω$ ^ω + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢2 + ω⁢3, $ω$ ^ω + ω³⁢2 + ω⁢3 + 1, $ω$ ^ω + ω³⁢2 + ω⁢3 + 2, $ω$ ^ω + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω².

" $ω$ ^ω + ω³⁢2 + ω², $ω$ ^ω + ω³⁢2 + ω² + 1, $ω$ ^ω + ω³⁢2 + ω² + 2, $ω$ ^ω + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω² + ω.

" $ω$ ^ω + ω³⁢2 + ω² + ω, $ω$ ^ω + ω³⁢2 + ω² + ω + 1, $ω$ ^ω + ω³⁢2 + ω² + ω + 2, $ω$ ^ω + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω² + ω + ω.

" $ω$ ^ω + ω³⁢2 + ω² + ω⁢2, $ω$ ^ω + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^ω + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^ω + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢2 + ω² + ω⁢3, $ω$ ^ω + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^ω + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^ω + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω² + ω².

" $ω$ ^ω + ω³⁢2 + ω²⁢2, $ω$ ^ω + ω³⁢2 + ω²⁢2 + 1, $ω$ ^ω + ω³⁢2 + ω²⁢2 + 2, $ω$ ^ω + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^ω + ω³⁢2 + ω²⁢3, $ω$ ^ω + ω³⁢2 + ω²⁢3 + 1, $ω$ ^ω + ω³⁢2 + ω²⁢3 + 2, $ω$ ^ω + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢2 + ω³.

" $ω$ ^ω + ω³⁢3, $ω$ ^ω + ω³⁢3 + 1, $ω$ ^ω + ω³⁢3 + 2, $ω$ ^ω + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω.

" $ω$ ^ω + ω³⁢3 + ω, $ω$ ^ω + ω³⁢3 + ω + 1, $ω$ ^ω + ω³⁢3 + ω + 2, $ω$ ^ω + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω + ω.

" $ω$ ^ω + ω³⁢3 + ω⁢2, $ω$ ^ω + ω³⁢3 + ω⁢2 + 1, $ω$ ^ω + ω³⁢3 + ω⁢2 + 2, $ω$ ^ω + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢3 + ω⁢3, $ω$ ^ω + ω³⁢3 + ω⁢3 + 1, $ω$ ^ω + ω³⁢3 + ω⁢3 + 2, $ω$ ^ω + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω².

" $ω$ ^ω + ω³⁢3 + ω², $ω$ ^ω + ω³⁢3 + ω² + 1, $ω$ ^ω + ω³⁢3 + ω² + 2, $ω$ ^ω + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω² + ω.

" $ω$ ^ω + ω³⁢3 + ω² + ω, $ω$ ^ω + ω³⁢3 + ω² + ω + 1, $ω$ ^ω + ω³⁢3 + ω² + ω + 2, $ω$ ^ω + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω² + ω + ω.

" $ω$ ^ω + ω³⁢3 + ω² + ω⁢2, $ω$ ^ω + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^ω + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^ω + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢3 + ω² + ω⁢3, $ω$ ^ω + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^ω + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^ω + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω² + ω².

" $ω$ ^ω + ω³⁢3 + ω²⁢2, $ω$ ^ω + ω³⁢3 + ω²⁢2 + 1, $ω$ ^ω + ω³⁢3 + ω²⁢2 + 2, $ω$ ^ω + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^ω + ω³⁢3 + ω²⁢3, $ω$ ^ω + ω³⁢3 + ω²⁢3 + 1, $ω$ ^ω + ω³⁢3 + ω²⁢3 + 2, $ω$ ^ω + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω + ω³⁢3 + ω³.

" $ω$ ^ω⁢2, $ω$ ^ω⁢2 + 1, $ω$ ^ω⁢2 + 2, $ω$ ^ω⁢2 + 3, ... ".

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

" $ω$ ^ω⁢2 + ω, $ω$ ^ω⁢2 + ω + 1, $ω$ ^ω⁢2 + ω + 2, $ω$ ^ω⁢2 + ω + 3, ... ".

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

" $ω$ ^ω⁢2 + ω⁢2, $ω$ ^ω⁢2 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω⁢2 + 3, ... ".

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

" $ω$ ^ω⁢2 + ω⁢3, $ω$ ^ω⁢2 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω².

" $ω$ ^ω⁢2 + ω², $ω$ ^ω⁢2 + ω² + 1, $ω$ ^ω⁢2 + ω² + 2, $ω$ ^ω⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω² + ω.

" $ω$ ^ω⁢2 + ω² + ω, $ω$ ^ω⁢2 + ω² + ω + 1, $ω$ ^ω⁢2 + ω² + ω + 2, $ω$ ^ω⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω² + ω + ω.

" $ω$ ^ω⁢2 + ω² + ω⁢2, $ω$ ^ω⁢2 + ω² + ω⁢2 + 1, $ω$ ^ω⁢2 + ω² + ω⁢2 + 2, $ω$ ^ω⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω² + ω⁢3, $ω$ ^ω⁢2 + ω² + ω⁢3 + 1, $ω$ ^ω⁢2 + ω² + ω⁢3 + 2, $ω$ ^ω⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω² + ω².

" $ω$ ^ω⁢2 + ω²⁢2, $ω$ ^ω⁢2 + ω²⁢2 + 1, $ω$ ^ω⁢2 + ω²⁢2 + 2, $ω$ ^ω⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢2 + ω.

" $ω$ ^ω⁢2 + ω²⁢2 + ω, $ω$ ^ω⁢2 + ω²⁢2 + ω + 1, $ω$ ^ω⁢2 + ω²⁢2 + ω + 2, $ω$ ^ω⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢2 + ω²⁢2 + ω⁢2, $ω$ ^ω⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω²⁢2 + ω⁢3, $ω$ ^ω⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢2 + ω².

" $ω$ ^ω⁢2 + ω²⁢3, $ω$ ^ω⁢2 + ω²⁢3 + 1, $ω$ ^ω⁢2 + ω²⁢3 + 2, $ω$ ^ω⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢3 + ω.

" $ω$ ^ω⁢2 + ω²⁢3 + ω, $ω$ ^ω⁢2 + ω²⁢3 + ω + 1, $ω$ ^ω⁢2 + ω²⁢3 + ω + 2, $ω$ ^ω⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢2 + ω²⁢3 + ω⁢2, $ω$ ^ω⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω²⁢3 + ω⁢3, $ω$ ^ω⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³.

" $ω$ ^ω⁢2 + ω³, $ω$ ^ω⁢2 + ω³ + 1, $ω$ ^ω⁢2 + ω³ + 2, $ω$ ^ω⁢2 + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω.

" $ω$ ^ω⁢2 + ω³ + ω, $ω$ ^ω⁢2 + ω³ + ω + 1, $ω$ ^ω⁢2 + ω³ + ω + 2, $ω$ ^ω⁢2 + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω + ω.

" $ω$ ^ω⁢2 + ω³ + ω⁢2, $ω$ ^ω⁢2 + ω³ + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³ + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³ + ω⁢3, $ω$ ^ω⁢2 + ω³ + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³ + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω².

" $ω$ ^ω⁢2 + ω³ + ω², $ω$ ^ω⁢2 + ω³ + ω² + 1, $ω$ ^ω⁢2 + ω³ + ω² + 2, $ω$ ^ω⁢2 + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω² + ω.

" $ω$ ^ω⁢2 + ω³ + ω² + ω, $ω$ ^ω⁢2 + ω³ + ω² + ω + 1, $ω$ ^ω⁢2 + ω³ + ω² + ω + 2, $ω$ ^ω⁢2 + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω² + ω + ω.

" $ω$ ^ω⁢2 + ω³ + ω² + ω⁢2, $ω$ ^ω⁢2 + ω³ + ω² + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³ + ω² + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³ + ω² + ω⁢3, $ω$ ^ω⁢2 + ω³ + ω² + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³ + ω² + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω² + ω².

" $ω$ ^ω⁢2 + ω³ + ω²⁢2, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω.

" $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢2, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢3, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢2 + ω².

" $ω$ ^ω⁢2 + ω³ + ω²⁢3, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω.

" $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢2, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢3, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³ + ω³.

" $ω$ ^ω⁢2 + ω³⁢2, $ω$ ^ω⁢2 + ω³⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω, $ω$ ^ω⁢2 + ω³⁢2 + ω + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω⁢2, $ω$ ^ω⁢2 + ω³⁢2 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω⁢3, $ω$ ^ω⁢2 + ω³⁢2 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω².

" $ω$ ^ω⁢2 + ω³⁢2 + ω², $ω$ ^ω⁢2 + ω³⁢2 + ω² + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω² + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢2, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢3, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω² + ω².

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢2 + ω³.

" $ω$ ^ω⁢2 + ω³⁢3, $ω$ ^ω⁢2 + ω³⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω, $ω$ ^ω⁢2 + ω³⁢3 + ω + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω⁢2, $ω$ ^ω⁢2 + ω³⁢3 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω⁢3, $ω$ ^ω⁢2 + ω³⁢3 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω².

" $ω$ ^ω⁢2 + ω³⁢3 + ω², $ω$ ^ω⁢2 + ω³⁢3 + ω² + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω² + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢2, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢3, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω² + ω².

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢2 + ω³⁢3 + ω³.

" $ω$ ^ω⁢3, $ω$ ^ω⁢3 + 1, $ω$ ^ω⁢3 + 2, $ω$ ^ω⁢3 + 3, ... ".

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

" $ω$ ^ω⁢3 + ω, $ω$ ^ω⁢3 + ω + 1, $ω$ ^ω⁢3 + ω + 2, $ω$ ^ω⁢3 + ω + 3, ... ".

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

" $ω$ ^ω⁢3 + ω⁢2, $ω$ ^ω⁢3 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω⁢2 + 3, ... ".

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

" $ω$ ^ω⁢3 + ω⁢3, $ω$ ^ω⁢3 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω⁢3 + 3, ... ".

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

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω².

" $ω$ ^ω⁢3 + ω², $ω$ ^ω⁢3 + ω² + 1, $ω$ ^ω⁢3 + ω² + 2, $ω$ ^ω⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω² + ω.

" $ω$ ^ω⁢3 + ω² + ω, $ω$ ^ω⁢3 + ω² + ω + 1, $ω$ ^ω⁢3 + ω² + ω + 2, $ω$ ^ω⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω² + ω + ω.

" $ω$ ^ω⁢3 + ω² + ω⁢2, $ω$ ^ω⁢3 + ω² + ω⁢2 + 1, $ω$ ^ω⁢3 + ω² + ω⁢2 + 2, $ω$ ^ω⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω² + ω⁢3, $ω$ ^ω⁢3 + ω² + ω⁢3 + 1, $ω$ ^ω⁢3 + ω² + ω⁢3 + 2, $ω$ ^ω⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω² + ω².

" $ω$ ^ω⁢3 + ω²⁢2, $ω$ ^ω⁢3 + ω²⁢2 + 1, $ω$ ^ω⁢3 + ω²⁢2 + 2, $ω$ ^ω⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢2 + ω.

" $ω$ ^ω⁢3 + ω²⁢2 + ω, $ω$ ^ω⁢3 + ω²⁢2 + ω + 1, $ω$ ^ω⁢3 + ω²⁢2 + ω + 2, $ω$ ^ω⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢3 + ω²⁢2 + ω⁢2, $ω$ ^ω⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω²⁢2 + ω⁢3, $ω$ ^ω⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢2 + ω².

" $ω$ ^ω⁢3 + ω²⁢3, $ω$ ^ω⁢3 + ω²⁢3 + 1, $ω$ ^ω⁢3 + ω²⁢3 + 2, $ω$ ^ω⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢3 + ω.

" $ω$ ^ω⁢3 + ω²⁢3 + ω, $ω$ ^ω⁢3 + ω²⁢3 + ω + 1, $ω$ ^ω⁢3 + ω²⁢3 + ω + 2, $ω$ ^ω⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢3 + ω²⁢3 + ω⁢2, $ω$ ^ω⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω²⁢3 + ω⁢3, $ω$ ^ω⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³.

" $ω$ ^ω⁢3 + ω³, $ω$ ^ω⁢3 + ω³ + 1, $ω$ ^ω⁢3 + ω³ + 2, $ω$ ^ω⁢3 + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω.

" $ω$ ^ω⁢3 + ω³ + ω, $ω$ ^ω⁢3 + ω³ + ω + 1, $ω$ ^ω⁢3 + ω³ + ω + 2, $ω$ ^ω⁢3 + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω + ω.

" $ω$ ^ω⁢3 + ω³ + ω⁢2, $ω$ ^ω⁢3 + ω³ + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³ + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³ + ω⁢3, $ω$ ^ω⁢3 + ω³ + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³ + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω².

" $ω$ ^ω⁢3 + ω³ + ω², $ω$ ^ω⁢3 + ω³ + ω² + 1, $ω$ ^ω⁢3 + ω³ + ω² + 2, $ω$ ^ω⁢3 + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω² + ω.

" $ω$ ^ω⁢3 + ω³ + ω² + ω, $ω$ ^ω⁢3 + ω³ + ω² + ω + 1, $ω$ ^ω⁢3 + ω³ + ω² + ω + 2, $ω$ ^ω⁢3 + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω² + ω + ω.

" $ω$ ^ω⁢3 + ω³ + ω² + ω⁢2, $ω$ ^ω⁢3 + ω³ + ω² + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³ + ω² + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³ + ω² + ω⁢3, $ω$ ^ω⁢3 + ω³ + ω² + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³ + ω² + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω² + ω².

" $ω$ ^ω⁢3 + ω³ + ω²⁢2, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω.

" $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢2, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢3, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢2 + ω².

" $ω$ ^ω⁢3 + ω³ + ω²⁢3, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω.

" $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢2, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢3, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³ + ω³.

" $ω$ ^ω⁢3 + ω³⁢2, $ω$ ^ω⁢3 + ω³⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω, $ω$ ^ω⁢3 + ω³⁢2 + ω + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω⁢2, $ω$ ^ω⁢3 + ω³⁢2 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω⁢3, $ω$ ^ω⁢3 + ω³⁢2 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω².

" $ω$ ^ω⁢3 + ω³⁢2 + ω², $ω$ ^ω⁢3 + ω³⁢2 + ω² + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω² + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢2, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢3, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω² + ω².

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢2 + ω³.

" $ω$ ^ω⁢3 + ω³⁢3, $ω$ ^ω⁢3 + ω³⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω, $ω$ ^ω⁢3 + ω³⁢3 + ω + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω⁢2, $ω$ ^ω⁢3 + ω³⁢3 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω⁢3, $ω$ ^ω⁢3 + ω³⁢3 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω².

" $ω$ ^ω⁢3 + ω³⁢3 + ω², $ω$ ^ω⁢3 + ω³⁢3 + ω² + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω² + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢2, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢3, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω² + ω².

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^ω⁢3 + ω³⁢3 + ω³.

" $ω$ ^{ω + 1}, $ω$ ^{ω + 1} + 1, $ω$ ^{ω + 1} + 2, $ω$ ^{ω + 1} + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω.

" $ω$ ^{ω + 1} + ω, $ω$ ^{ω + 1} + ω + 1, $ω$ ^{ω + 1} + ω + 2, $ω$ ^{ω + 1} + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω + ω.

" $ω$ ^{ω + 1} + ω⁢2, $ω$ ^{ω + 1} + ω⁢2 + 1, $ω$ ^{ω + 1} + ω⁢2 + 2, $ω$ ^{ω + 1} + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω⁢3, $ω$ ^{ω + 1} + ω⁢3 + 1, $ω$ ^{ω + 1} + ω⁢3 + 2, $ω$ ^{ω + 1} + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω².

" $ω$ ^{ω + 1} + ω², $ω$ ^{ω + 1} + ω² + 1, $ω$ ^{ω + 1} + ω² + 2, $ω$ ^{ω + 1} + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω² + ω.

" $ω$ ^{ω + 1} + ω² + ω, $ω$ ^{ω + 1} + ω² + ω + 1, $ω$ ^{ω + 1} + ω² + ω + 2, $ω$ ^{ω + 1} + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω² + ω + ω.

" $ω$ ^{ω + 1} + ω² + ω⁢2, $ω$ ^{ω + 1} + ω² + ω⁢2 + 1, $ω$ ^{ω + 1} + ω² + ω⁢2 + 2, $ω$ ^{ω + 1} + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω² + ω⁢3, $ω$ ^{ω + 1} + ω² + ω⁢3 + 1, $ω$ ^{ω + 1} + ω² + ω⁢3 + 2, $ω$ ^{ω + 1} + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω² + ω².

" $ω$ ^{ω + 1} + ω²⁢2, $ω$ ^{ω + 1} + ω²⁢2 + 1, $ω$ ^{ω + 1} + ω²⁢2 + 2, $ω$ ^{ω + 1} + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢2 + ω.

" $ω$ ^{ω + 1} + ω²⁢2 + ω, $ω$ ^{ω + 1} + ω²⁢2 + ω + 1, $ω$ ^{ω + 1} + ω²⁢2 + ω + 2, $ω$ ^{ω + 1} + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1} + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1} + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1} + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢2 + ω².

" $ω$ ^{ω + 1} + ω²⁢3, $ω$ ^{ω + 1} + ω²⁢3 + 1, $ω$ ^{ω + 1} + ω²⁢3 + 2, $ω$ ^{ω + 1} + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢3 + ω.

" $ω$ ^{ω + 1} + ω²⁢3 + ω, $ω$ ^{ω + 1} + ω²⁢3 + ω + 1, $ω$ ^{ω + 1} + ω²⁢3 + ω + 2, $ω$ ^{ω + 1} + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1} + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1} + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1} + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³.

" $ω$ ^{ω + 1} + ω³, $ω$ ^{ω + 1} + ω³ + 1, $ω$ ^{ω + 1} + ω³ + 2, $ω$ ^{ω + 1} + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω.

" $ω$ ^{ω + 1} + ω³ + ω, $ω$ ^{ω + 1} + ω³ + ω + 1, $ω$ ^{ω + 1} + ω³ + ω + 2, $ω$ ^{ω + 1} + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω + ω.

" $ω$ ^{ω + 1} + ω³ + ω⁢2, $ω$ ^{ω + 1} + ω³ + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³ + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³ + ω⁢3, $ω$ ^{ω + 1} + ω³ + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³ + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω².

" $ω$ ^{ω + 1} + ω³ + ω², $ω$ ^{ω + 1} + ω³ + ω² + 1, $ω$ ^{ω + 1} + ω³ + ω² + 2, $ω$ ^{ω + 1} + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω² + ω.

" $ω$ ^{ω + 1} + ω³ + ω² + ω, $ω$ ^{ω + 1} + ω³ + ω² + ω + 1, $ω$ ^{ω + 1} + ω³ + ω² + ω + 2, $ω$ ^{ω + 1} + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω² + ω + ω.

" $ω$ ^{ω + 1} + ω³ + ω² + ω⁢2, $ω$ ^{ω + 1} + ω³ + ω² + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³ + ω² + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³ + ω² + ω⁢3, $ω$ ^{ω + 1} + ω³ + ω² + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³ + ω² + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω² + ω².

" $ω$ ^{ω + 1} + ω³ + ω²⁢2, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω.

" $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢2 + ω².

" $ω$ ^{ω + 1} + ω³ + ω²⁢3, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω.

" $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³ + ω³.

" $ω$ ^{ω + 1} + ω³⁢2, $ω$ ^{ω + 1} + ω³⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω, $ω$ ^{ω + 1} + ω³⁢2 + ω + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω⁢2, $ω$ ^{ω + 1} + ω³⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω⁢3, $ω$ ^{ω + 1} + ω³⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω².

" $ω$ ^{ω + 1} + ω³⁢2 + ω², $ω$ ^{ω + 1} + ω³⁢2 + ω² + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω² + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢2, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢3, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω² + ω².

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢2 + ω³.

" $ω$ ^{ω + 1} + ω³⁢3, $ω$ ^{ω + 1} + ω³⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω, $ω$ ^{ω + 1} + ω³⁢3 + ω + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω⁢2, $ω$ ^{ω + 1} + ω³⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω⁢3, $ω$ ^{ω + 1} + ω³⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω².

" $ω$ ^{ω + 1} + ω³⁢3 + ω², $ω$ ^{ω + 1} + ω³⁢3 + ω² + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω² + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢2, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢3, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω² + ω².

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1} + ω³⁢3 + ω³.

" $ω$ ^{ω + 1}⁢2, $ω$ ^{ω + 1}⁢2 + 1, $ω$ ^{ω + 1}⁢2 + 2, $ω$ ^{ω + 1}⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω, $ω$ ^{ω + 1}⁢2 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω².

" $ω$ ^{ω + 1}⁢2 + ω², $ω$ ^{ω + 1}⁢2 + ω² + 1, $ω$ ^{ω + 1}⁢2 + ω² + 2, $ω$ ^{ω + 1}⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω² + ω.

" $ω$ ^{ω + 1}⁢2 + ω² + ω, $ω$ ^{ω + 1}⁢2 + ω² + ω + 1, $ω$ ^{ω + 1}⁢2 + ω² + ω + 2, $ω$ ^{ω + 1}⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω² + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω² + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω² + ω².

" $ω$ ^{ω + 1}⁢2 + ω²⁢2, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢2 + ω²⁢3, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³.

" $ω$ ^{ω + 1}⁢2 + ω³, $ω$ ^{ω + 1}⁢2 + ω³ + 1, $ω$ ^{ω + 1}⁢2 + ω³ + 2, $ω$ ^{ω + 1}⁢2 + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω, $ω$ ^{ω + 1}⁢2 + ω³ + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω².

" $ω$ ^{ω + 1}⁢2 + ω³ + ω², $ω$ ^{ω + 1}⁢2 + ω³ + ω² + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω² + ω².

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³ + ω³.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω².

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω², $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω² + ω².

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢2 + ω³.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω².

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω², $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω² + ω².

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢2 + ω³⁢3 + ω³.

" $ω$ ^{ω + 1}⁢3, $ω$ ^{ω + 1}⁢3 + 1, $ω$ ^{ω + 1}⁢3 + 2, $ω$ ^{ω + 1}⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω.

" $ω$ ^{ω + 1}⁢3 + ω, $ω$ ^{ω + 1}⁢3 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω².

" $ω$ ^{ω + 1}⁢3 + ω², $ω$ ^{ω + 1}⁢3 + ω² + 1, $ω$ ^{ω + 1}⁢3 + ω² + 2, $ω$ ^{ω + 1}⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω² + ω.

" $ω$ ^{ω + 1}⁢3 + ω² + ω, $ω$ ^{ω + 1}⁢3 + ω² + ω + 1, $ω$ ^{ω + 1}⁢3 + ω² + ω + 2, $ω$ ^{ω + 1}⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω² + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω² + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω² + ω².

" $ω$ ^{ω + 1}⁢3 + ω²⁢2, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢3 + ω²⁢3, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³.

" $ω$ ^{ω + 1}⁢3 + ω³, $ω$ ^{ω + 1}⁢3 + ω³ + 1, $ω$ ^{ω + 1}⁢3 + ω³ + 2, $ω$ ^{ω + 1}⁢3 + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω, $ω$ ^{ω + 1}⁢3 + ω³ + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω².

" $ω$ ^{ω + 1}⁢3 + ω³ + ω², $ω$ ^{ω + 1}⁢3 + ω³ + ω² + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω² + ω².

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³ + ω³.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω².

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω², $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω² + ω².

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢2 + ω³.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω².

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω², $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω² + ω².

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 1}⁢3 + ω³⁢3 + ω³.

" $ω$ ^{ω + 2}, $ω$ ^{ω + 2} + 1, $ω$ ^{ω + 2} + 2, $ω$ ^{ω + 2} + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω.

" $ω$ ^{ω + 2} + ω, $ω$ ^{ω + 2} + ω + 1, $ω$ ^{ω + 2} + ω + 2, $ω$ ^{ω + 2} + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω + ω.

" $ω$ ^{ω + 2} + ω⁢2, $ω$ ^{ω + 2} + ω⁢2 + 1, $ω$ ^{ω + 2} + ω⁢2 + 2, $ω$ ^{ω + 2} + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω⁢3, $ω$ ^{ω + 2} + ω⁢3 + 1, $ω$ ^{ω + 2} + ω⁢3 + 2, $ω$ ^{ω + 2} + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω².

" $ω$ ^{ω + 2} + ω², $ω$ ^{ω + 2} + ω² + 1, $ω$ ^{ω + 2} + ω² + 2, $ω$ ^{ω + 2} + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω² + ω.

" $ω$ ^{ω + 2} + ω² + ω, $ω$ ^{ω + 2} + ω² + ω + 1, $ω$ ^{ω + 2} + ω² + ω + 2, $ω$ ^{ω + 2} + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω² + ω + ω.

" $ω$ ^{ω + 2} + ω² + ω⁢2, $ω$ ^{ω + 2} + ω² + ω⁢2 + 1, $ω$ ^{ω + 2} + ω² + ω⁢2 + 2, $ω$ ^{ω + 2} + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω² + ω⁢3, $ω$ ^{ω + 2} + ω² + ω⁢3 + 1, $ω$ ^{ω + 2} + ω² + ω⁢3 + 2, $ω$ ^{ω + 2} + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω² + ω².

" $ω$ ^{ω + 2} + ω²⁢2, $ω$ ^{ω + 2} + ω²⁢2 + 1, $ω$ ^{ω + 2} + ω²⁢2 + 2, $ω$ ^{ω + 2} + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢2 + ω.

" $ω$ ^{ω + 2} + ω²⁢2 + ω, $ω$ ^{ω + 2} + ω²⁢2 + ω + 1, $ω$ ^{ω + 2} + ω²⁢2 + ω + 2, $ω$ ^{ω + 2} + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2} + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2} + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2} + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢2 + ω².

" $ω$ ^{ω + 2} + ω²⁢3, $ω$ ^{ω + 2} + ω²⁢3 + 1, $ω$ ^{ω + 2} + ω²⁢3 + 2, $ω$ ^{ω + 2} + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢3 + ω.

" $ω$ ^{ω + 2} + ω²⁢3 + ω, $ω$ ^{ω + 2} + ω²⁢3 + ω + 1, $ω$ ^{ω + 2} + ω²⁢3 + ω + 2, $ω$ ^{ω + 2} + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2} + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2} + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2} + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³.

" $ω$ ^{ω + 2} + ω³, $ω$ ^{ω + 2} + ω³ + 1, $ω$ ^{ω + 2} + ω³ + 2, $ω$ ^{ω + 2} + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω.

" $ω$ ^{ω + 2} + ω³ + ω, $ω$ ^{ω + 2} + ω³ + ω + 1, $ω$ ^{ω + 2} + ω³ + ω + 2, $ω$ ^{ω + 2} + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω + ω.

" $ω$ ^{ω + 2} + ω³ + ω⁢2, $ω$ ^{ω + 2} + ω³ + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³ + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³ + ω⁢3, $ω$ ^{ω + 2} + ω³ + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³ + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω².

" $ω$ ^{ω + 2} + ω³ + ω², $ω$ ^{ω + 2} + ω³ + ω² + 1, $ω$ ^{ω + 2} + ω³ + ω² + 2, $ω$ ^{ω + 2} + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω² + ω.

" $ω$ ^{ω + 2} + ω³ + ω² + ω, $ω$ ^{ω + 2} + ω³ + ω² + ω + 1, $ω$ ^{ω + 2} + ω³ + ω² + ω + 2, $ω$ ^{ω + 2} + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω² + ω + ω.

" $ω$ ^{ω + 2} + ω³ + ω² + ω⁢2, $ω$ ^{ω + 2} + ω³ + ω² + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³ + ω² + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³ + ω² + ω⁢3, $ω$ ^{ω + 2} + ω³ + ω² + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³ + ω² + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω² + ω².

" $ω$ ^{ω + 2} + ω³ + ω²⁢2, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω.

" $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢2 + ω².

" $ω$ ^{ω + 2} + ω³ + ω²⁢3, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω.

" $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³ + ω³.

" $ω$ ^{ω + 2} + ω³⁢2, $ω$ ^{ω + 2} + ω³⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω, $ω$ ^{ω + 2} + ω³⁢2 + ω + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω⁢2, $ω$ ^{ω + 2} + ω³⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω⁢3, $ω$ ^{ω + 2} + ω³⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω².

" $ω$ ^{ω + 2} + ω³⁢2 + ω², $ω$ ^{ω + 2} + ω³⁢2 + ω² + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω² + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢2, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢3, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω² + ω².

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢2 + ω³.

" $ω$ ^{ω + 2} + ω³⁢3, $ω$ ^{ω + 2} + ω³⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω, $ω$ ^{ω + 2} + ω³⁢3 + ω + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω⁢2, $ω$ ^{ω + 2} + ω³⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω⁢3, $ω$ ^{ω + 2} + ω³⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω².

" $ω$ ^{ω + 2} + ω³⁢3 + ω², $ω$ ^{ω + 2} + ω³⁢3 + ω² + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω² + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢2, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢3, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω² + ω².

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2} + ω³⁢3 + ω³.

" $ω$ ^{ω + 2}⁢2, $ω$ ^{ω + 2}⁢2 + 1, $ω$ ^{ω + 2}⁢2 + 2, $ω$ ^{ω + 2}⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω, $ω$ ^{ω + 2}⁢2 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω².

" $ω$ ^{ω + 2}⁢2 + ω², $ω$ ^{ω + 2}⁢2 + ω² + 1, $ω$ ^{ω + 2}⁢2 + ω² + 2, $ω$ ^{ω + 2}⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω² + ω.

" $ω$ ^{ω + 2}⁢2 + ω² + ω, $ω$ ^{ω + 2}⁢2 + ω² + ω + 1, $ω$ ^{ω + 2}⁢2 + ω² + ω + 2, $ω$ ^{ω + 2}⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω² + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω² + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω² + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω² + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω² + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω² + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω² + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω² + ω².

" $ω$ ^{ω + 2}⁢2 + ω²⁢2, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢2 + ω².

" $ω$ ^{ω + 2}⁢2 + ω²⁢3, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω.

" $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³.

" $ω$ ^{ω + 2}⁢2 + ω³, $ω$ ^{ω + 2}⁢2 + ω³ + 1, $ω$ ^{ω + 2}⁢2 + ω³ + 2, $ω$ ^{ω + 2}⁢2 + ω³ + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω, $ω$ ^{ω + 2}⁢2 + ω³ + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω².

" $ω$ ^{ω + 2}⁢2 + ω³ + ω², $ω$ ^{ω + 2}⁢2 + ω³ + ω² + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω² + ω².

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢2 + ω².

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³ + ω³.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω².

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω², $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω² + ω².

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢2 + ω².

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢2 + ω³.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω².

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω², $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω² + ω².

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢2 + ω².

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω²⁢3 + ω².

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢2 + ω³⁢3 + ω³.

" $ω$ ^{ω + 2}⁢3, $ω$ ^{ω + 2}⁢3 + 1, $ω$ ^{ω + 2}⁢3 + 2, $ω$ ^{ω + 2}⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω.

" $ω$ ^{ω + 2}⁢3 + ω, $ω$ ^{ω + 2}⁢3 + ω + 1, $ω$ ^{ω + 2}⁢3 + ω + 2, $ω$ ^{ω + 2}⁢3 + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω + ω.

" $ω$ ^{ω + 2}⁢3 + ω⁢2, $ω$ ^{ω + 2}⁢3 + ω⁢2 + 1, $ω$ ^{ω + 2}⁢3 + ω⁢2 + 2, $ω$ ^{ω + 2}⁢3 + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢3 + ω⁢3, $ω$ ^{ω + 2}⁢3 + ω⁢3 + 1, $ω$ ^{ω + 2}⁢3 + ω⁢3 + 2, $ω$ ^{ω + 2}⁢3 + ω⁢3 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω⁢3 + ω.

...

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω².

" $ω$ ^{ω + 2}⁢3 + ω², $ω$ ^{ω + 2}⁢3 + ω² + 1, $ω$ ^{ω + 2}⁢3 + ω² + 2, $ω$ ^{ω + 2}⁢3 + ω² + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω² + ω.

" $ω$ ^{ω + 2}⁢3 + ω² + ω, $ω$ ^{ω + 2}⁢3 + ω² + ω + 1, $ω$ ^{ω + 2}⁢3 + ω² + ω + 2, $ω$ ^{ω + 2}⁢3 + ω² + ω + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω² + ω + ω.

" $ω$ ^{ω + 2}⁢3 + ω² + ω⁢2, $ω$ ^{ω + 2}⁢3 + ω² + ω⁢2 + 1, $ω$ ^{ω + 2}⁢3 + ω² + ω⁢2 + 2, $ω$ ^{ω + 2}⁢3 + ω² + ω⁢2 + 3, ... ".

Eventually he ran out of natural numbers again. That didn't stop him. He'd just use $ω$ ^{ω + 2}⁢3 + ω² + ω⁢2 + ω.

" $ω$ ^{ω + 2}⁢3 + ω² + ω⁢3, $ω$ ^{ω + 2}⁢3 + ω² + ω⁢3 + 1, $<$