eli5 How does Euclid’s theorem prove that there are infinite prime numbers.

Question

eli5 How does Euclid’s theorem prove that there are infinite prime numbers.

In: Mathematics

Answer 1

It’s a proof by contradiction. You assume something, then show that the assumption leads to a contradiction, which means the assumption must be false. In that proof, you assume there’s a complete list of primes, and use that assumption to show that the list is incomplete. That’s a contradiction, so the assumption that there’s a complete list of primes must be false.