Fact
Some infinities are bigger than others
There are more numbers between 0 and 1 than there are whole numbers, and it can be proved in a paragraph.
Cantor showed the real numbers cannot be put in one-to-one correspondence with the integers: assume you have listed them all, then construct a new number differing from the first in its first digit, the second in its second, and so on. The result is not on your list. So the reals form a strictly larger infinity.