Fermat's Last theorem short proof
in [Math]
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From: bassam king karzeddin on 5 May 2007 22:48 > >What I had been working for many years was about the > most >general theorem...: > >For any triangle of positive, distinct, INTEGER > SIDES > >(L>M>S), there exists a positive real number (P>=1), > such >that the following equation holds true always > >S^P + M^P = L^P > > Your "theorem" is a first year (may be first month) > calculus exercise: > Assume 0<r,s<1. Prove that > f(x)=r^x+s^x-1 > has a (unique) positive root. > Proof: lim_x=0+ f(x)=1, lim_x=+infinity f(x)=-1. By > continuity there is p in ]0,inf[ such that f(p)=0. > Uniqueness (hint): Prove that f'(x)<0. Yes of course, but the question is not at all about the existence of the real P that satisfies the equation The question is about the EXACT value of P The question is about the type and the nature of the real number P The question is much far behind the existence of P Regards Bassam Karzeddin Al Hussein bin Talal University JORDAN
From: bassam king karzeddin on 9 May 2007 07:16 > >What I had been working for many years was about the > most >general theorem...: > >For any triangle of positive, distinct, INTEGER > SIDES > >(L>M>S), there exists a positive real number (P>=1), > such >that the following equation holds true always > >S^P + M^P = L^P > > Your "theorem" is a first year (may be first month) > calculus exercise: > Assume 0<r,s<1. Prove that > f(x)=r^x+s^x-1 > has a (unique) positive root. > Proof: lim_x=0+ f(x)=1, lim_x=+infinity f(x)=-1. By > continuity there is p in ]0,inf[ such that f(p)=0. > Uniqueness (hint): Prove that f'(x)<0. By the way Did they teach you HOW to find P rather than it's existence only? Or is there a direct formula for P? Can you imagine how the world will change immeadiatly if a direct formula for P is obtained? Regards B.Karzeddin
From: hagman on 9 May 2007 15:15 On 9 Mai, 17:16, bassam king karzeddin <bas...(a)ahu.edu.jo> wrote: > > >What I had been working for many years was about the > > most >general theorem...: > > >For any triangle of positive, distinct, INTEGER > > SIDES > > >(L>M>S), there exists a positive real number (P>=1), > > such >that the following equation holds true always > > >S^P + M^P = L^P > > > Your "theorem" is a first year (may be first month) > > calculus exercise: > > Assume 0<r,s<1. Prove that > > f(x)=r^x+s^x-1 > > has a (unique) positive root. > > Proof: lim_x=0+ f(x)=1, lim_x=+infinity f(x)=-1. By > > continuity there is p in ]0,inf[ such that f(p)=0. > > Uniqueness (hint): Prove that f'(x)<0. > > By the way > > Did they teach you HOW to find P rather than it's existence only? > Or is there a direct formula for P? > > Can you imagine how the world will change immeadiatly if a direct formula for P is obtained? Yes: Not at all
From: bassam king karzeddin on 11 May 2007 01:53 > On 9 Mai, 17:16, bassam king karzeddin > <bas...(a)ahu.edu.jo> wrote: > > > >What I had been working for many years was about > the > > > most >general theorem...: > > > >For any triangle of positive, distinct, INTEGER > > > SIDES > > > >(L>M>S), there exists a positive real number > (P>=1), > > > such >that the following equation holds true > always > > > >S^P + M^P = L^P > > > > > Your "theorem" is a first year (may be first > month) > > > calculus exercise: > > > Assume 0<r,s<1. Prove that > > > f(x)=r^x+s^x-1 > > > has a (unique) positive root. > > > Proof: lim_x=0+ f(x)=1, lim_x=+infinity f(x)=-1. > By > > > continuity there is p in ]0,inf[ such that > f(p)=0. > > > Uniqueness (hint): Prove that f'(x)<0. > > > > By the way > > > > Did they teach you HOW to find P rather than it's > existence only? > > Or is there a direct formula for P? > > > > Can you imagine how the world will change > immeadiatly if a direct formula for P is obtained? > > Yes: Not at all > Indeed, Not at all.... Regards B.Karzeddin
From: bassam king karzeddin on 11 May 2007 03:48
Dear All I would like to add my PRIMITIVE definition of any real positive number (excluding one) in simple mathematical concepts hoping that is nonsense In words Any positive real number other than one can be represented as a product of all the prime numbers, where each prime number exponent is an integer number In symbols, Let P be the set of Prime Numbers, let Z be the set of Integer Numbers, let R be the set of Real Numbers, then any positive real number ( r_I = / 1) where (r_I belongs to R) can be represented as the following: r_I = Product {I=1 to I = Infy}(p_I)^(z_I}, Where (p_I) belongs to P, and (z_I) belongs to Z Observations: The rational numbers are well distributed and have the same density in any segment of real number line, also having finite set of prime numbers when excluding all other prime factors with exponents equal to zero The Irrational numbers must have infinite prime factors that have non-zero integer exponent Any negative comments, references, suggestions are welcomed Regards Bassam Karzeddin Al Hussein bin Talal University JORDAN |