"Fermat's Last Theorem" Disproved?
in [Math]
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From: cjcountess on 15 Jul 2010 18:11 I find this interesting from bert A few points for you, which previous answerers may have, I think, not made completely clear: (1) Mathematicians separate "numbers" into several categories: integer, rational, irrational, algebraic, transcendental. You don't, and you should have. (2) Fermat's Last Theorem applies to INTEGERS (and by a simple mathematical argument, also to rationals). The numbers in your counter-example are algebraic, so it doesn't apply to FLT. (3) Just for your interest, the Pythagorean example with the diagonal of a square is one which has no solution in integers or rationals, only in algebraic numbers. This was proved by Euclid about 500 BC, and G.H. Hardy in his autobiographical "A Mathematician's Apology" quotes the proof as an example of what mathematics is about and how it's really done. (4) Similarly, what Andrew Wiles has proved is that while Fermat's equation has solutions in algebraic numbers (which you have also shown), it has none in integers or in rationals. This from Chip Eastham Apart from the OP's failure to construct solutions of a^3 + b^3 = c^3, there is also Conrad's failure to address the requirement that a,b,c be nonzero integers. Certainly nonzero real a,b,c exist that solve the equation, even if Conrad's geometry does not correspond to a solution. --c and this from smallfrey In 1897, Hilbert proved that Fermat's equation for "regular" prime exponents has only the trivial solution in the cyclotomic field Q(zeta). So, even saying there are real solutions is dicey. The above examples may point me in the right direction of finding a legit proof, as well as let me know to take into account the restrictions to the theorems. Although my example was the wrong one, except if I can prove that a cube is the square of a square, which indirectly might disprove the theorem, I suspected that there is an exception to this rule somewhere. But if the square of a square is a forth power instead of a cube, than how is that geometrically shaped. It does not even exist except conceptually, unless you consider the forth dimension to be time. I have seen equations of relativity (E^2=m^2c^4+p^2v^2) which use the Pythagorean theorem, and includes a forth power. Would this exclude Fermats Theorem? Probably not, since people probably took that into account, and re defined the theorem. Fermat himself could not have known of it, since it is a recent discovery compared to Fermat's time and I dought he would have fashioned his theorem around it Conrad J Countess
From: Virgil on 15 Jul 2010 18:31 In article <a6884a8b-575a-4100-b682-b638e557fbf8(a)i28g2000yqa.googlegroups.com>, cjcountess <cjcountess(a)yahoo.com> wrote: > Although my example was the wrong one, except if I can prove that �a > cube is the square of a square�, which indirectly might disprove the > theorem, I suspected that there is an exception to this rule > somewhere. In the real number system, -8 is a cube which is not even a square, much less the square of a square.
From: Frederick Williams on 15 Jul 2010 19:12 cjcountess wrote: > But if the square of a square is a forth power instead of a cube, than > how is that geometrically shaped. It does not even exist except > conceptually, unless you consider the forth dimension to be time. Don't confuse the "n" in "x to the power n" with the n-th dimension of physical space-time. -- I can't go on, I'll go on.
From: Tim Little on 16 Jul 2010 03:16 On 2010-07-15, cjcountess <cjcountess(a)yahoo.com> wrote: > And as I traced the measurement of energy from E=hf/c^2 to E=mc^2, > one can see that the energy moves from a relatively straight line at > its lowest form, to waves that contract, gaining energy > exponentially. I find Archimedes Plutonium to be much more interesting in the position of combined math/physics crackpot than you. Though not all is lost, you could contend with BURT for the position of incoherent comic relief. - Tim
From: cjcountess on 16 Jul 2010 16:17
Tim So do I, I find Archimedes Plutonium very intertaining and intelegent, and bold enougth to propose the idea of the universe as an atom. There is much more truth in such an intertaining analogy than many realize. But tell me, What is your claim to fame, What is your contribution to the knowlendge base of humanity, What is your realization or revolution, that can contribute to the shining of light of discovery on reality? Or are you just a pest mascarading as a threat. I discovered that (E=mc^2 = E=mc^circled and/or sphered), and (c= natural unite, sqrt of natural unite -1) or electron, and that (h/2pi/ 2) is no longer measure of uncertainty, it is the certain measure of an electron, thereby cancelling out "uncertainty principle, renomalization, runing coupling constants problem, complex inacurate dimensional analisis, and a host of other problems to list some of its practical aplications. as well as bringing (sqrt -1) out of realm of imaginary numbers, into real world of real numbers. Analogous to (a line of 1 inch in linear direction x a line of 1 inch in 90 degree angular direction, c in the linear direction x c in 90 degree angular direction = c^2), as a balence of "centripital/ centrifugal", forces. resulting in circular and or spherical rotation and rest mass. Therefor the EM or electromagnetic spectrum, is also the EM or energy/ matter spectrum. Give Achie some respect, he is a bold thinker, and more right about some things than people give him credit for, and so am I. This "Fermat's Theorem" chalenge, was something I did off the top of my head, and I admit I made a mistake in the chosing of examples. But I have discovered something else that you may not have been aware of because of it which I will share shortly with the group. I am not afraid to question statements that I suspect, not afraid to sugest new ideas, and certainly not afraid of critisism from weak people like you, who have nothing to say but critisism Conrad J Countess |