applying Goldbach proof format to FLT and Riemann Hypothesis #683: Correcting Math
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From: Archimedes Plutonium on 15 Jul 2010 15:40 Archimedes Plutonium wrote: > I am just fresh off of proving infinitude of Mersenne primes by using > the Indirect Euclid Infinitude of Primes > proof method where W+1 and W-1 captures two new necessarily prime > Euclid Numbers. So, fresh off of that > experience led me tonight to think of Goldbach's Conjecture. > > Now let me recite some of my past history on working > on the Goldbach Conjecture before I give this simple proof. I like to > cite or recite the history because it shows us that if we are in a > state of thinking about something, we can see what links were there to > make the new thoughts. > > I thought I had proven the Goldbach Conjecture circa > 1991 or thereabouts and set up partitions. Such as this partition for > the number 8. > > 0 8 > 1 7 > 2 6 > 3 5 > 4 4 > > Now I set up partitions like that for all even numbers > and the argument that I posed for a proof was that notice where the 3 > and the 5 for 3+5 = 8. My proof argument was that one side of the > partition had to contain a prime number as well as the other side due > to a theorem that between n and 2n exists a prime number. Great so > far, now all I needed was some way of saying that every even number > had a prime lined up from one side that lines up with the prime on the > second side, just like the 3 lines up with the 5 above. > > So I hunted around in 1991 and came up with the idea that I multiply > those lined up numbers and that led me > to the idea that if Goldbach was false, then composite numbers that > had only two prime factors such as 3x5 = > 15 that if Goldbach was false, then at least one number that is > uniquely decomposed by the Fundamental theorem of Arithmetic into two > prime factors does not exist. > > Well, that is alot of lining up and someone in sci.math > in the 2000s pointed out that this was no proof. And I argeed with > him. > > But tonight I offer a brand new attack. It retains some bits and > pieces of my old attack. > > Proof of Goldbach Conjecture that every even number larger than 2 is > the sum of two primes. > > Proof: This is an Algebra Proof and requires the translation of > addition into multiplication. In other words, we replace addition by > multiplication from the > fancy Galois theory of Algebra of groups, rings, field etc. Every even > number beyond 2 is decomposable by multiplication by at least two > primes. So that 4 is 2 x 2, > and that 6 is 2x3 and that 8 is 2 x 2 x 2. So hold on a minute here. > The number 8 maybe strange looking but remember in Goldbach with > addition that 4 = 2 + 2 to satisfy Goldbach. For Multiplication that 8 > is 2 x 2 x 2 > is no encumbrance to the idea that every even number has at least two > prime factors, even though the number > 8 has three prime factors. You see, I am switching into a Goldbach for > addition to a Goldbach for multiplication > and a Goldbach for multiplication would simply say that Every Even > Number has at Least Two Prime Factors, but it probably has more in > many cases. I am letting the Structure of Algebra to convert addition > to the operator of multiplication. So, now, all I need is to note that > Every Even Number must have at least two prime factors. That is > obviously true, because every even number has "2" as a prime factor so > then every even number must have another prime factor and thus must > have At Least Two Prime Factors. Now, get the Algebra Galois Machinery > or Framework and switch over from Multiplication to Addition. It is > known from Algebra that the operators are interchangeable. So the > proving mechanism boils down to this. If Goldbach is false, then there > exists an even number larger than 2 which does not have two prime > factors in multiplication. > QED > > Comments: I have always felt that when a math conjecture is easy to > communicate and easy to understand by almost anyone, that the proof of > the conjecture must also be a simple idea proof. A conjecture such as > Riemann Hypothesis which is inaccessible to anyone not a > mathematician, would have a complex proof. But a conjecture that is > accessible to grade-school children, then the proof of it > in the end is as simple as it is accessible. > > However, in the above, the proof relies on Algebra theory that > multiplication is interchangeable with addition, and that is a complex > idea and theory and proof. > Alright, in the above, offers key insights into other math conjectures and why they are never proveable because mathematicians fail to precision define what they mean by finite-number versus infinite-number. Mathematics should and would have a simple quick proof of Fermat's Last Theorem, FLT and the Riemann Hypothesis if the boundary line between finite and infinite is given as 10^500. Then all proof methods in mathematics are Direct or Constructive proofs and we can resort to Indirect only when lazy and not wanting a accurate proof. I say "not wanting an accurate proof" because in the Indirect Method we pit all of mathematics, its entire house of axioms and proven theorems into one big gambit, but that gambit is from Aristotelian straight line linear logic, and the broader world where mathematics is only a part of Physics, logic becomes duality logic and nonlinear. So the Indirect Method in mathematics is to be avoided as much as possible for it is unreliable. That is why it is imperative to precision define the boundary between finite number and infinite number, so that all the proofs of mathematics are Direct Method proofs. All of the fake proofs in modern mathematics today such as Wiles's FLT, and the Appel & Haken 4 Color Mapping and the recent Poincare Conjecture and the recent Kepler Packing are all fake proofs hidden in an Indirect Method. Once you define Finite number as all numbers below 10^500 and infinite as 10^500 or larger (inverse for 10^-500), you immediately recognize that Poincare Conjecture is a false conjecture and no proof ever will become of it since there must be no absolute continuity and that there are holes and gaps when going smaller than 10^-500. For FLT and Riemann Hypothesis (RH), if infinity is 10^500 or larger then these two conjectures are true and can be easily proven true with Construction proofs. But under the current imprecision of the mathematics community over finite number versus infinite number there never can be proofs of those two conjectures. Now let me apply the same proof technique of Goldbach to that of FLT and RH. For the RH, well it already has a Algebra of its elements of multiplication versus addition. But looking at FLT and suppose we render it from addition: a^n + b^n = c^n And render that into multiplication: a^n(b^n) = (c^n) Now we instantly recognize that the multiplication has solutions for all exponents in Natural Numbers. 10^3(100^3) = 1000^3 So we ask, since we have this simple proof for Goldbach by simply interchanging the ALGEBRA of addition to multiplication, we ask why can we easily prove Goldbach but never prove FLT. And the answer is really quite simple. When you refuse to define the boundary between finite number and infinite number, that such a dereliction of the job of defining does not hinder the proof of Goldbach, but it surely hinders the proof of FLT and RH. The reason that there are solutions to the multiplication of FLT and not addition is because there are solutions to the addition of FLT for we have boatloads of p- adics that solve FLT only we refuse to recognize that Wiles assumed the Natural Numbers are not infinite integers when they are if you do not define the boundary. So when we apply the Goldbach technique to FLT, we find that FLT really has solutions to all exponents such as these solutions: The expression a^n+b^n=c^n is true for all n, given the following values. a= ...9977392256259918212890625 b= ...0022607743740081787109376 c= ...0000000000000000000000001 When mathematicians fail to do their job properly, fail to define what it means to be a finite number and not a infinite number then they come up with fake Wiles proofs. Also, I should mention that the reason the Appel & Haken and the recent alleged Kepler Packing are fake proofs is because of more ill-definitions in those problems for the Jordan Curve theorem proves 4 Color Mapping which is really just 2 Color Mapping since borderlines should not be ignored. As for Kepler Packing, the concept of packing infinite space is really a mockery to precision definition. Packing means containment or container. So once you add into the Kepler Packing Problem the idea of a container of various sizes and for which there is a optimal packing, then you have a precision- conjecture, not a obfuscated foggy mess of a idea. Kepler Packing as infinity is like expecting a math proof of the conjecture that "brown color is cool". 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 |