For instance, the set of all integers is smaller than the set of all reals, as proven by Georg Cantor in his Diagonal Proof :) Integer infinity is called countable infinity, aka aleph null. Infinity of the reals is called uncountable infinity. Countable because you can start with the smallest number and work your way to infinity. Uncountable because . ̅01 ("point zero repeating, with a 1 at the end") is not a valid number. You can't start with the smallest possible nonzero positive number. It's just not possible. Thus it's uncountable.
Is it bad I spent 10 minutes just trying to get the unicode to work for the overline? xD Even then not sure why it didn't parse correctly.
