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Feb 11, 2011 at 22:57 comment added Michael Hardy ....other way to phrase this is not a proof by contradiction. Yet it had just said "we have to argue by contradiction". This is a place where the book could be improved by omitting something. The proof by contradiction (which, contrary to the assertions of many universally respected authors, is not in the works of Euclid) should just be omitted. The "other way to phrase this argument", which proves that we do not "have to argue by contradiction" is in fact the one in Euclid's Elements.
Feb 11, 2011 at 22:55 comment added Michael Hardy It showed up today. It looks excellent so far. But there's something really weird on pages 114--115. For the proof of the infinitude of primes, it says on page 114 "we will have to argue by contradiction". That is of course nonsense, and then the usual proof by contradiction, which is pointlessly complicated, is given on page 115. Then it says "Another way to phrase this argument would be the following. Suppose we have any finite collection of primes" etc..... It shows that if you multiply them and add 1 and then factor the result, you get primes not in the set you started with. This
Feb 4, 2011 at 0:56 comment added Michael Hardy Thank you. I've requested Gross & Harris via interlibrary loan.
Feb 1, 2011 at 3:59 history edited Daniel Litt CC BY-SA 2.5
mis-spelled oeuvre
Feb 1, 2011 at 3:56 history made wiki Post Made Community Wiki by S. Carnahan
Feb 1, 2011 at 3:47 history answered Daniel Litt CC BY-SA 2.5