Harold Edwards publish a Euclid IP proof? Address of Mathematical Intelligencer? #610 Correcting Math
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From: Archimedes Plutonium on 28 Jun 2010 15:15 David Bernier wrote: > Archimedes Plutonium wrote: > >> [0] Michael *Hardy* and Catherine Woodgold, > >> "*Prime* *Simplicity*", *Mathematical > >> Intelligencer<https://mail.google.com/wiki/Mathematical_Intelligencer> > > > > > > I was contacted that the above has Archimedes Plutonium's ideas > > published in Mathematical Intelligencer. > > > The authors write that Euclid's proof that there is no largest > prime number is a constructive one. They mention several > forms of distortions that misrepresent the proof, for example > those who say that Euclid's proof was a proof by contradiction. > > Harold Edwards wrote a letter to the Editors showing his > enthusiasm at having the proof presented as it appears > in the Elements. > > Cf.: > < http://www.springerlink.com/content/m0t8727288823ug5/ > > > > [first page only to non-subscribers]. > > David Bernier Funny how they say get your information faster on the Internet. But when it comes to basics such as a mailing address for Mathematical Intelligencer MI, one has to run to an actual hardcopy. Hard for me to understand Harold Edwards enthusiasm for finally exposing the truth about whether Euclid's Infinitude of Primes (IP) proof was direct or indirect, when according to Wikipedia that Mr. Edwards had enthusiasm for the fake proof of Fermat's Last Theorem of Wiles, considering it is a fake proof because Wiles never defines what is the difference between a finite number and an infinite number. You see, in mathematics, if you leave the question unanswered as to when numbers become infinite numbers and no longer are finite numbers, then you end up with a whole gaggle of statements that can never be proven true or false. I am not talking about undecidability, but am talking about, simply precision of definition which is the main job of mathematics in the first place. Fermat's Last Theorem has boatloads of numbers that satisfy a^n + b^n = c^n to any exponent when a number is ambiguous as to whether it is finite or infinite. The Peano Axioms never well-defines the difference between a finite number and an infinite number. Ask anyone what finite number means and then ask them whether .....33333 is finite. According to Peano axioms and Fermat's Last Theorem the number .....33333 is as finite as the number 3 because the Peano axioms never tells us where finite ends and infinite begins. And this is the reason Goldbach Conjecture, Fermat's Last Theorem, Twin Primes, Riemann Hypothesis have no proof, nor will they ever be proven so long as noone in math gives a **precision definition of finite versus infinite number**. Some people may think, oh well AP is just complaining, but then look at geometry where they do well-define a finite line as a line segment and a infinite line as a line ray or a ray infinite in both directions. If Geometry is wise enough to well define finite line from infinite line, then why is number theorists too dumb and too stupid to well define finite number from infinite number? Is it because, well, too many mathematicians will have the shame of pie in their face? Now I did give a precision definition of finite number versus infinite number and it is the only way to go on this chore. I used the king of science-- physics, because physics contains all of mathematics as a tiny subset of itself. In physics, numbers give out at 10^500 for integers. That number is so huge, that their is nothing in physics of the Planck Units that makes any physical sense. But mathematicians are really not very bright and not very smart of a class of people. Mathematicians in large part are lemmings and parrots who follow fashion trends of any given century rather than follow Physics and Logic. If you define Finite as all the numbers smaller than 10^500, you instantly clear out all of those Number theory problems unsolved and unsolvable. Now it sounds as though I am pretty harsh on mathematicians and on Harold Edwards, which according to Wikipedia Mr. Edwards is a founder of the magazine Mathematical Intelligencer. But I am not harsh enough, because mathematics has progressed so far, so fast, but it cannot even address and correct something as old as Euclid's Infinitude of Primes proof when such is under scrutiny. Mathematics is too much of a old man's clubhouse that entrenches fake math. And Mr. Edwards is part of that problem itself. Did Edwards ever write out a Euclid Infinitude of Primes proof in one of his books? I would guess he did. And I would further guess that Edwards was never bright enough to do both the direct and indirect method of proof. No, I would guess that Edwards, as a founder of MI, was not even bright enough to ask some writer to expose both a valid direct and valid indirect proof of IP in a MI issue. About the only brightness of Edwards concerning Euclid's IP is to get some authors to talk about a statistics of how many thought Euclid's IP was constructive or contradiction. A statistical expose of how many mathematicians voted constructive rather than contradiction. That is not really much progress but it is snail's pace progress. A bright editor, on the other hand would have summoned someone to write a article exposing what the valid Euclid IP constructive versus the valid Euclid IP contradiction methods looked like. Edwards was not bright enough for such a project, because, probably, Edwards was never able to give a valid Euclid contradiction proof himself. To give a valid Euclid contradiction method proof means you must say in the proof that the Euclid Number is necessarily prime, otherwise your attempt is an invalid proof. Edwards probably never could see that, and so we have at best from MI a statistical article, or a roll-call of how many mathematicians think Euclid IP is constructive "please raise your hands". We don't have an Edwards in control of the situation. An Edwards who wants the "real and whole truth" about Euclid's Infinitude of Primes, who is not a scaredy-cat about printing a valid direct alongside a valid indirect. Why do we not have that? Because obviously, about 90% of all those mathematicians who ever wrote down a Euclid IP in book or print form, have a mangled and garbled mess and invalid proof. Imagine that, 90% flunking in a Euclid IP proof. That is worse, by far than a freshman Calculus class on a surprize quiz. The Internet and newsgroups such as sci.math is helping mathematics by training our focus away from magazines and publications, which is a good thing. Because the major reason that math is so slow in correcting itself and why math has fakeries such as Cantor infinities and Godel nonsense and Wiles FLT, is that fakeries can hide behind entrenched math publications. The Internet is "open to all" and admittedly most of the Internet is worthless nonsense, but the small percentage of the best of the Internet quickens the pace of fake math being exposed. Fake math that hides behind entrenched journal writings. We now have the question of whether Euclid IP is direct or indirect by this article of Hardy/Woodgold/MI. But the deeper question as to "could any mathematician prior to 1993, ever give a valid Euclid IP indirect?" I say noone prior to 1993, realized that Euclid's Number must necessarily be prime for the proof to be valid. So, does Edwards have the audacity, the integrity to have a writeup in Mathematical Intelligencer exposing the fact, the idea that only when Euclid's Number is necessarily prime that you have a valid reductio ad absurdum proof of Infinitude of Primes? Does Edwards measure up to the contest of valid indirect method? Can someone please post the mailing address of Mathematical Intelligencer. 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
From: sttscitrans on 28 Jun 2010 15:37
On 28 June, 20:15, Archimedes Plutonium <plutonium.archime...(a)gmail.com> wrote: > David Bernier wrote: > > Archimedes Plutonium wrote: > > >> [0] Michael *Hardy* and Catherine Woodgold, > > >> "*Prime* *Simplicity*", *Mathematical > To give a valid Euclid contradiction method proof means you must say > in the proof that the > Euclid Number is necessarily prime, otherwise your attempt is an > invalid proof. I see you still have not grasped a few simple ideas. 1) Every natural greater than 1 has a prime divisor 2) GCD(n,n+1) = 1 3) If there is a last prime then GCD(w,w+1) <> 1 Contradiction. Therefore, the number of primes is infinite Presumably even you can see that 1) and 2) are true statements and that the assumption that primes are finite in number leads to the contradiction GCD(w,w+1) <> 1 The necessity of "necessary primes" is simply a delusion on your part |