>>11520420
infinity is wrong. It has 1 use, and it's not as a number.
It's to describe the size of the set of all integers.
[math][\underbrace{0,1,2,3,4,5,\dots}_{\infty} ][/math]
it has no well defined application outside of this, and this is just the axiom of infinity. Because of it's sole usage here, this is functionally truly no different than it being the "Axiom of Endlessness" or "Axiom of Unlimited", cause it's no different than saying
[math][\underbrace{0,1,2,3,4,5,\dots}_{\text{unlimited}} ][/math].
Nothing about it defines it can be used as an actual number, meaning
[math]\infty - \infty = undefined \\ \frac{n}{\infty} = undefined \\ \infty * n = undefined \\ \infty \pm n = undefined \\ 0^{\infty} = undefined[/math]
if you want to define any of these, you have to show where they are defined to work as such, and whether or not that definition relies on the presence of the axiom of infinity; otherwise provide examples where a case must be defined to solve a problem, thus providing a proof.