the theory of infinite sets. Cantor used it to prove that there are exactly as many positive fractions (ratios p/q of positive whole numbers p and q) as there are natural numbers (1, 2, 3, 4, . . .). That’s a much stronger statement than saying both sets are infinite. It says they are infinite to precisely the same extent, in the sense that a one-to-one correspondence can be established between them.
