[FOM] Infinity of primes in Euclid

Mark Bridger mark_bridger at yahoo.com
Thu Dec 15 09:33:12 EST 2005

Euclid does NOT say that there are infinitely many primes. Rather, he proves that for any number of primes there must be another. The reference is: Book IX, Proposition 20: "Prime numbers are more than any assigned multitude of prime numbers." ("The History of Mathematics - A Reader" ed. J. Fauvel, J. Gray.)
  This is an example of Aristotle's "Potential Infinity" as opposed to a "Completed Infinity."
  M. Bridger

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