Fermat's Last theorem short proof
in [Math]
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From: bassam king karzeddin on 12 May 2007 15:26 >>Hello quasi > >>Thanks for your notes, about this thread I think it is still in the beginning, and I shall make it hopefully a story as you may see later how all the correct methods intersect at only one fact >>About the definition is certainly a primitive >A primitive? What does that mean? I have plans to make it much simpler, but not completed yet >since the reals are already defined, your claim about >the positive >reals is definitely a conjecture until proved or >disproved. The proof Any rational number can be expressed as the ratio of two integer numbers that are coprime to each others, where each of them has distinct prime factorizations, and when the two integers become infinite but having a certain ratio, then they produce some kind of finite rational and all kinds of irrational numbers, and that make the whole set of real numbers, where I think it is too easy now to make the symbolic proof >>The concept may extend also to express any non-zero real number E, where >> (E = M*C^2), and (M) is real number that has a prime >>factors to exponent (+/- 1) only, (C) is real number That may be a multiple of Sqrt (-1) >what you are saying here is that once one has such an >infinite >product, one can extract a squarefree part. Sure, >that's true. In >fact, the exponents of the squarefree part can all be 1 >(no need for -1). What I mean is that Energy can never be equal to zero We can't exclude (-1) exponent, see for a counter example the real number (1/63) = (7^ (-1))*(3^ (-2) >However, there doesn't have to be a nontrivial square >free part since >every positive real is already a square. Thus, all the >exponents for >the primes can be forced to be even. Every positive integer is already a square, I wish to believe that, As a counter example PI is not a square number as I do remember, unless I miss something >>About the Irrational Numbers I mentioned the following: >> >>The Irrational numbers must have infinite prime >>factors that have non-zero integer exponent >True. >>And who is on earth could find the prime factors of Sqrt (2) for example!! >Careful here. >Those exponents are not unique. EVERY NON-ZERO real number MUST have UNIQUE factorization >there are infinitely many different factorizations of >sqrt (2) that >match your specification. That is only an approximation to any large number of digits I suppose, but never exactly >Also, you need to take note of my correction. For the >positive >irrationals, the infinite products do not converge. In >that sense, you >can't even talk about an infinite product. However it >is possible to >force a unique accumulation point for the subsequence >of partial >products. If we extend the concept of infinite products >to allow the >value of such a product to be the value of the unique >accumulation >point (if any), then your claim of such a >representation becomes >valid. Still, as mentioned above, the representation is >definitely not >unique. But why not converging once you have the infinite prime factors acting to unique powerS and from both earth and sky and taking you always to the endless mysterious dangerous puzzle of Sqrt(2) >>If my definition works then what is the deference >>between Sqrt (2) and PI or (e=2.71…), except in our >>elementary WRONG fundamental theorem of algebra. >With the extended concept of infinite products as >discussed above, all >positive reals can be represented as an infinite >product of prime >powers with integer exponents. >That doesn't in any way contradict the Fundamental >Theorem of Algebra. I'm afraid I feel it DOES, I hope to prove it rigorously >As an analogy, consider the fact that every positive >real can be >written as a nonnegative integer plus an infinite >decimal. The numbers >sqrt (2), Pi, and e all have such decimal >representations. Thus, the >fact of having an infinite, non-repeating decimal >representation does >not, by itself, give any information as to whether an >irrational >number is algebraic or transcendental. Yes, see for example you may express any real number as a sum of integer number and sin(x), but the main problem is the prime numbers or angles themselves (little information) >>Still I have to verify and explain something else in >>mind before I hunt the darkness about the imaginary >>numbers, >Be careful. Many hunters enter the dark world of >imaginary numbers but >never return. Thanks for the warning, I know it is a hell dangerous area that few can go in, but I can't help it, I feel I was born for that and I shall be glad to die for it >>and who knows if I'm mistaken (hopefully YES) >Hopefully no. >Unfortunately, probably yes. I guess you are the mainly one here who can penetrate others so easily Regards B.Karzeddin quasi
From: bassam king karzeddin on 12 May 2007 15:44 > > bassam king karzeddin wrote: > > > But, he immediately concluded that N can't be an > INTEGER NUMBER > > > > Therefore he could DARE to announce and tell his > famous conjecture on a very solid proof bases, but > alas who was there to listen, although > > He didn't announce it, or give a proof. > But, You got his proof now, Don't YOU really ??!! Regards B.Karzeddin
From: quasi on 12 May 2007 21:30 On Sat, 12 May 2007 19:26:15 EDT, bassam king karzeddin <bassam(a)ahu.edu.jo> wrote: >>>About the Irrational Numbers I mentioned the following: >>> >>>The Irrational numbers must have infinite prime >>factors that have non-zero integer exponent > >>True. > >>>And who is on earth could find the prime factors of Sqrt (2) for example!! > >>Careful here. > >>Those exponents are not unique. > >EVERY NON-ZERO real number MUST have UNIQUE factorization Good luck on that. You have uncountably many real numbers so you'll need uncountably many factorizations. Thus, if you specify prime factors with integer exponents, the factorization can't be unique. quasi
From: bassam king karzeddin on 12 May 2007 17:03 > On Sat, 12 May 2007 19:26:15 EDT, bassam king > karzeddin > <bassam(a)ahu.edu.jo> wrote: > > >>>About the Irrational Numbers I mentioned the > following: > >>> > >>>The Irrational numbers must have infinite prime > >>factors that have non-zero integer exponent > > > >>True. > > > >>>And who is on earth could find the prime factors > of Sqrt (2) for example!! > > > >>Careful here. > > > >>Those exponents are not unique. > > > >EVERY NON-ZERO real number MUST have UNIQUE > factorization > > Good luck on that. You have uncountably many real > numbers so you'll > need uncountably many factorizations. Thus, if you > specify prime > factors with integer exponents, the factorization > can't be unique. > > quasi I got your point quasi with examples I think I have learnt something important from you. Thanks a lot quasi B.Karzeddin
From: Denis Feldmann on 13 May 2007 04:59
quasi a �crit : > On Sat, 12 May 2007 19:26:15 EDT, bassam king karzeddin > <bassam(a)ahu.edu.jo> wrote: > >>>> About the Irrational Numbers I mentioned the following: >>>> >>>> The Irrational numbers must have infinite prime >>factors that have non-zero integer exponent >>> True. >>>> And who is on earth could find the prime factors of Sqrt (2) for example!! >>> Careful here. >>> Those exponents are not unique. >> EVERY NON-ZERO real number MUST have UNIQUE factorization > > Good luck on that. You have uncountably many real numbers so you'll > need uncountably many factorizations. Thus, if you specify prime > factors with integer exponents, the factorization can't be unique. Lots of logical mistakes, here : precisely because you need *too many* of them, they will probablyt be unique or none. Then, we are speaking of infinite products, so there are actually uncountable many of them. > > quasi |