Q: How do you talk about the size of infinity? How can one infinity be bigger than another?
All of the infinities so far have been “countably infinite”, because they’re the same “size” as the counting numbers. The size of the set of real numbers is an example of a larger infinity. There’s no way to pair the real numbers up with the counting numbers (it’s difficult to show this). The kind of infinity that’s the size of the set of real numbers is called “ “. Quick aside: If A is a set, then the power set of A (written 2A, for silly reasons) is the “set of all subsets of A”.