A proper job by Mathematical Intelligencer covering the errors of Euclid's infinitude of primes proof; how it would look #605 Correcting Math
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From: Archimedes Plutonium on 26 Jun 2010 20:37 > > So I doubt that Hardy or Moongold knows what a valid Euclid IP by > contraction is. And they Typing too fast, obviously for that should read "contradiction" not contraction and my mind is between physics and math so I can see how that error slip came about. I corrected in the original with a (sic) sign. But let me just briefly comment on how a logical article to Mathematical Intelligencer MI would have read over this issue. It would have given the construction proof in the first paragraph, noting how it increases set cardinality. In the second paragraph it would have displayed the proof by contradiction, and the key lines in the proof that makes alot of math professors go wrong and most every one in the general public go into error is the line that says that the Euclid Number-- all the primes in existence multiplied together and add 1 is necessarily prime itself. In the Contradiction proof of infinitude of primes, what makes it so difficult is that P+ 1 is necessarily prime due to the formalism of the logical setup. Both Hardy and Moongold and even GH Hardy were unable to recognize that this was the foul up or the stumbling block of nearly everyone who ventures into a Euclidean IP by contradiction. They make the error and then they try to defend themselves with the silly example of 1+2x3x5x7x11x13 = 59x509. In the proof by Contradiction that number is necessarily prime because you assumed the primes were finite and so 59 x 509 is necessarily prime given your assumption. This is what trips up so many people, even Hardy and Moongold and a long list of professors of mathematics. That in the proof by contradiction the number P+1 is necessarily prime. And neither Hardy nor Moongold made that clear. And since they failed to make that clear, they had no right to lambast their long list of math professors who made mistakes. It is true that Euclid's proof was a constructive proof or direct proof. But the Mathematical Intelligencer article was far to shoddy and lacking in logic to make clear the errors of Euclid's Infinitude of Primes by Contradiction. And I do not appreciate Mathematical Intelligencer stealing the bulk of my ideas on Euclid's Infinitude of Primes proof. Actually, I am glad that alot of magazines of science and especially math are going out of business due to people getting information over the Internet instead. The old magazine peer review was mostly a clubhouse society that was biased and prejudicial and very unfair to alot of authors. The worst case I have seen is where my friend from Stanford submitted a article only to be rejected and only to see his ideas and math being included in another article of a different author. In other words, the journal stole his work. And my friend never really recovered from that incident. Archimedes Plutonium http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |