On Sun, Oct 11, 2020, 9:07 PM Steven D'Aprano 
Even in the cardinal numbers, two times infinity (aleph-0) is just aleph-0; however you might be pleased to know that two to the power of aleph-0 is aleph-1.

Oh... So you're one of those who believe the Continuum Hypothesis :-).

I was going to mention Surreal Numbers also, but I see you touched on it.