Fermat's Polygonal Number theorem vs FLT?
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From: fernando revilla on 7 May 2010 10:02 Jesse F. Hughes wrote > Do you think there is an isomorphism between N and R > or not? ThinkTank has explained it a non denumerable number of times. --- http://ficus.pntic.mec.es/~frej0002/
From: ThinkTank on 7 May 2010 10:10 > Jesse F. Hughes wrote > > > Do you think there is an isomorphism between N and > R > > or not? > > ThinkTank has explained it a non denumerable number > of times. > Thank you, Fernando! :-) > --- > http://ficus.pntic.mec.es/~frej0002/
From: Arturo Magidin on 7 May 2010 14:34 On May 7, 12:11 pm, ThinkTank <ebigl...(a)gmail.com> wrote: > > It's certainly possible that you *misspoke* when you > > said "an > > isomorphism between the integers and the reals". > > Get your facts straight. See my response to Pubkeybreaker. I have seen no response, to Pubkeybreaker or anyone else, where you expound or explain what you meant when you mentioned an "isomorphism between the integers and the reals". Perhaps you can give the Message ID number, since there are at least three replies of yours to Pubkeybreaker in this thread alone, and relative statements like "below" depend on exactly what newsreader you are using. Now, which "facts" did I get wrong? (i) You did *not* speak of an "isomorphism between the integers and the reals"? Alas, you did. It's right here, on message http://groups.google.com/group/sci.math/msg/036fb0ce02daa8dd where you said, and I quote: "However, I have developed a completely different proof, which does not rely on either of these, but rather on Galois fields, and an isomorphism between the integers and the reals. It is a complete proof, however, I may have made a mistake somewhere, so I am checking it. " There is it: "[relies on] an isomorphism between the integers and the reals". So that's not a fact I got wrong. (ii) That there can be no isomorphism between the integers and the reals? No, that's also a fact: there can be *no isomorphism of any kind* between the integers and the reals, for the simple reason that the integers and the reals are not even bijectable (they cannot be put in one-to-one, onto, correspondence). So that's not a fact I got wrong either. So I confess myself lost. Do set me straight and harangue me some more for not figuring out what you meant, and instead relying (in my usual stupid and superficial manner) on what you actually wrote. -- Arturo Magidin
From: Arturo Magidin on 7 May 2010 15:16 On May 7, 10:54 am, ThinkTank <ebigl...(a)gmail.com> wrote: > As I have > basically already pointed out, Fermat's little theorem: > > x^p == x (mod p) > > could be regarded as a statement about the symmetry of > the figurate number x^p. Could you point me to the post in which you explained this? I don't think I understand but would be interested to see. If you can give me a link or a message ID that would be great; I haven't been able to find it, but searching in google is very spotty these days. > Furthermore, consider that the > rth coefficient of binomial expansion of x^p are is the > is the pth regular r-polytopic number. I also have trouble here. When I think of a binomial expansion, I think of a power of a sum, not a power of a single term (e.g., (a +b)^p, not a^p; perhaps you mean something like (x+kp)^p, perhaps thinking of x as a congruence class?) What is an r-polytopic number? -- Arturo Magidin
From: fernando revilla on 7 May 2010 11:23
Jesse F. Hughes wrote: > He has never explained what he meant when he said > that he had a proof > that relies on an isomorphism between N and R. Once more ( perhaps not the last one): Some of you should change the criticism about Think Tank proposal. He has explained upfrontly and indirectly that he meant: "There exists an isomorphism between IN and a subset of IR" --- http://ficus.pntic.mec.es/~frej0002/ |