Mathematical question, are there any infinite number systems?

Yes.

Alabama and Tennessee Pi are the only known ones.

There are an infinite number of them. It would take an infinite amount of time to prove it though.

As Kantor proved there is not ONE infinite but more
They have not one size but more than one, various or even infinite infinites, ones bigger than other ones
So it´s still speculative but not unthincable to imagine infinites that may work as "base" of others

Yes. Large digit tokenization in LLM treat base 1000 as valid, they behave different from base 10 in compute situations.

Most things exist because someone says it does..

Am I expected to question Stephen hawking? … 🤔🤷

idk why alabamians like you suddenly started to get interested in mathematics🙄

No arithmetical reason why not.

No

only when using the ammonia scrubber .000000009