Very impressive answer!
Might I suggest, though, (since I like to hock) that your example of infinity is a very low order infinity. If I’m not mistaken, the number of points on a two dimensional plane (or even a 3 space shape) is aleph-null. I believe it was Cantor who proved this.
Might not it be impossible for a higher order infinity to have finite properties? Certainly Hashem is the highest order infinte! If so, hadra kusha l’duchta.