ABSTRACT
Infinity is the lifeblood of mathematics, because there is no end to even the simplest mathematical objects-the positive integers 1, 2, 3, 4, 5, 6, 7, . . . . One of the oldest and best arguments about infinity is Euclid’s proof that the prime numbers 2, 3, 5, 7, 11, 13, . . . form an infinite sequence. Euclid succeeds despite knowing virtually nothing about the sequence, by showing instead that any finite sequence of primes is incomplete. That is, he shows how to find a prime p different from any given primes p1, p2, . . . , pn.
