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[HM] Infinity of primes in Euclid
Posted:
Dec 16, 2005 1:33 PM


If my memory is accurate, recently somebody (either at [FOM] or [HM] list) cited a similar attitude of Euclid to a line.
Something like that: Euclid never used the term 'infinite line', but used the term 'an unlimited line'.
This is also an example of Aristotle's "Potential Infinity" as opposed to an "Actual (Completed) Infinity".
Could anybody remind an exact citation of this point in Euclid?
Alexander Zenkin
Original Message From: Mark Bridger Sent: Thursday, December 15, 2005 5:33 PM To: fom@cs.nyu.edu Subject: [FOM] Infinity of primes in Euclid
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



