John Ramsden shines Re: grounds for dismissal of Julia F. Knight and Chandler Davis as math journal editors #5.10 Correcting Math
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From: Archimedes Plutonium on 10 Aug 2010 15:30 OwlHoot wrote: > On Aug 10, 5:32 pm, Archimedes Plutonium > <plutonium.archime...(a)gmail.com> wrote: > > > > So in words, the Euclid Infinitude of Primes proof, Indirect in > > short- > > form goes like this: > > > > 1) Definition of prime > > 2) Hypothetical assumption, suppose set of primes 2,3,5,7,.. is > > finite with P_k the last and final prime > > 3) Multiply the lot and add 1 (Euclid's number) which I call W+1 > > 4) W+1 is necessarily prime > > Not necessarily: W + 1 and W - 1, and for that matter any > integer V +/- W where V and W are any integers whose product > is divisible by all of 2, 3, 5, 7, .., P_k must be divisible > only by primes larger than P_k. > > But these "new" primes can divide those integers V +/- W to > a degree greater than 1, and there can be more than one of > them. > > The rest of the proof works in the same way though: > > > 5) contradiction to P_k as the last and largest prime > > 6) set of primes is infinite. > > > Cheers > > John Ramsden Hi John I do not want to argue with you or make you feel bad in any way. But the facts of your post and your followup of coprime, that you are mistaken. You must admit, that in all of your life of doing mathematics, you were never able to do a Infinitude of Twin Primes proof. I am certainly right on that, John. But the reason you were never able to do a Infinitude of Twin Primes proof, John Ramsden, is because you were never able to do a valid Infinitude of Regular Primes (Euclid style) Indirect Method. I do not mean to be hard on you John, but you mixed up the Indirect with the Direct method. So what I am saying, John, if that you had been able to do a proper and valid Euclid style Infinitude of Regular Primes Indirect method, you would also be able to prove the Infinitude of Twin Primes. Your mistake, John is that in the Indirect Method, the allying of both the definition of a prime number in step 1 with the hypothetical assumption step 2, those two steps when allied, forces W+1 and W-1 to be necessarily two new primes. For example, if the only primes that exist are 3 and 5, then Euclid's number of W+1 = 16 and W-1 = 14 are necessarily two new primes under that hypothetical space. If you cannot believe or understand what I am saying then try listening to Karl Heuer of 1994: Sun, 20FEB1994, 21:05:13 GMT sci.math INCONSISTENT PEANO AXIOMS AND MATH PROFESSORS Lines: 36 Sender: k...(a)spdcc.com (Karl Heuer) k...(a)ursa-major.spdcc.com (Karl Heuer) writes: In article (5JChA8g2...(a)jojo.escape.de> det...(a)jojo.escape.de (Detlef Bosau) writes: >Ludwig.Pluton...(a)dartmouth.edu meinte am 18.02.94 >>det...(a)jojo.escape.de (Detlef Bosau) writes: >>>Wrong. Your two numbers are not necessarily prime >>NO, YOU ARE WRONG. Those numbers are necessarily prime, due to >>UPFAT, all the primes that exist in the finite set leave a remainder >>of 1. >I'll give you a lesson of elementary arithmetics. . . I really shouldn't bother to get involved in this discussion again, but Ludwig is right. In logical terms, his key statement is "if P is a finite set containing all the primes, then prod(P)+1 is prime." This is a true statement. Let's step through your alleged counterexample: >consider your set of primes to be: {2,3,5,7,11,13}, as I assert 13 to be >the largest prime. [. . .] Now, you made the assertion, that > > > > (2x3x5x11x13) + 1 [=30031] must be prime. Yes, it's true that if 13 is the largest prime, then 30031 is prime. Do you disagree with that assertion? >As you stated before, there exists an unique prime decomposition of >30031. This is 59x509. It could be easily shown, that 59 and 509 >both are prime. If 13 is the largest prime, then 59x509 is not a factorization of 30031. --- end quoting Karl Heuer's post of 1994 --- So, Mr. John Ramsden, the reason that in all your math career in doing math, that you were never able to do a proof of the Infinitude of Twin Primes is very obvious why you could never do a Twin Primes proof, because you could never do a proper valid proof of Infinitude of Regular Primes, indirect method. Now maybe you can teach me something, John Ramsden. Because here we have a situation where mathematics offers us a proof of Infinitude of Regular Primes both Direct and Indirect Method. So the question that vexs me, is why would the Twin Primes only be amenable to a Indirect Method? Do proofs of mathematics have a sort of Physics conservation of energy principle attached. So that the energy of proving Regular Primes are infinite is exhausted and the only energy left in the entire logical system of mathematics is the energy for a "indirect method for twin-primes, Mersenne primes, and all the other related infinitude proofs? So I wonder if mathematics has a conservation principle that says some proofs can have both direct and indirect, but outlying conjectures must only have a indirect application? This is vexing, but I am sure it must be linked to physics. So, please, John Ramsden, please try to reconsider that you never, in your life ever gave a valid Euclid IP indirect, for if you had done so, perhaps in your youth, you would have immediately been able to prove infinitude of twin primes. Please, write out your indirect method of regular primes in a followup post. 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: OwlHoot on 11 Aug 2010 15:52
On Aug 10, 8:30 pm, Archimedes Plutonium <plutonium.archime...(a)gmail.com> wrote: > > [..] > > Hi John > > I do not want to argue with you or make you feel bad in any way. > But the facts of your post and your followup of coprime, that you > are mistaken. > > You must admit, that in all of your life of doing mathematics, you > were never able to do a Infinitude of Twin Primes proof. I am > certainly right on that, John. Yes, that's true. (But nobody else has either.) > But the reason you were never able to do a Infinitude of Twin Primes > proof, John Ramsden, is because you were never able to do a valid > Infinitude of Regular Primes (Euclid style) Indirect Method. I do > not mean to be hard on you John, but you mixed up the Indirect with > the Direct method. I may have misunderstood this, but I thought the (or "an") Indirect Method for proving an infinitude of primes, or for that matter the existence of anything that interests you, is to do this without having to construct examples explicitly. So if you mean something else, or there's something special about a Euclid style Indirect Method, then it would be best to define that. There are other methods, such as proving that the series of reciprocals of primes 1/2+1/3+1/5+ .. diverges. But unfortunately that doesn't work for prime pairs, because amazingly a guy called Brun proved that the sum of the reciprocals of these converges. One more point about my previous post. The reason the usual proof uses W +/- 1 as numbers divisible only by primes not dividing W, rather than V +/- W where V and W are coprime and V * W is divisible by all the first k primes is that V +/- W may equal -1 or 1. So you can't guarantee any new primes divide it! Cheers John Ramsden |