Fermat's Last Theorem simple proof impossible?
in [Math]
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From: DRMARJOHN on 22 May 2010 05:01 > On May 21, 11:54 pm, DRMARJOHN <MJOHN...(a)AOL.COM> > wrote: > > > There is a simple illustration to FLT.... > > > > There is the maxim Parallel lines converge at > infinity.... > > > > For FLT, when A^n + B^n = 1, (0<R<1) all real > numbers between 0 and 1... > > There are two sets of solutions.... > > There is a first A^n & B^n above and below .5.... > > There is a second A^n & B^n above and below .5.... > > There is a third A^n & B^n above and below .5.... > > ...There is an Nth A^n & B^n above and below > .5.... > > There are an infinite # of such pairs.... > > > > The second repeats the first set,.... > > > > Irrational roots have a Terminus at an infinite > point.... > > > > For the beginning pair, the first solution of .5 + > .5 = 1.... > > > > The character of the irrational base enables > success.... > > > > Only irrational roots give solutions.... > > > > Martin Johnson. > > > > It astounds me that the maxim parallel lines > converge at infinity.... > > Nowhere do you make any distinction between n = 3, > say, and n = 2. > Your argument seems t apply equally well to a^3 + b^3 > = 1 and to > a^2 + b^2 = 1. > So how do you account for (.6)^2 + (.8)^2 = 1? > Or (.384615384615384615,,,)^2 + > (.923076923076923076...)^2 = 1? > (that's (5/13)^2 + (12/13)^2 = 1). > -- > GM > The question of FLT is posed for n=3 and more. N of 3 is exponential. X^2 is straight line. That X^2 x X^2 = X^4 only gives the appearence that X^2 is in the same "family" as X^3. Humans created these conventions and the appearence of similarity does not make them the same. When you, a mathematician ask this kind of question, I, a novice, have to answer from a naive perspective, I have to figure it out in my own way, which may not have the language you are used to. I learned abou 3, 4, 5 in the illustration of a right triangle, with a visual flat plane. That 25 squares just does not expand into the three dimensional. In the examples I use: for .9^3, .9 x .9 = .81, .9 x .81 = .729. please bear with my primative illustrations. The square root of .729 is not .81. I say this because X^3 is X x X x X, and in the expansion of X to X^3 there is this intermediary step of X x X. The convention of one looks similar to the other, but an intermediary step does not -- well, like, One swallow does not make a spring. I sincerely appreciate your offering this question. You take with some seriousness my naive effort; my effort includes years of struggle and reading many books (almost all before 2003, when I put aside my work -- I have forgotten most of what I read, one reason my language is primitive.) I have crunched numbers for many hours in the past month -- so this latest approach is based on real numbers. I do not speculate from detached ideas. Martin Johnson
From: DRMARJOHN on 22 May 2010 05:29 > > > > In my imprecise way I suggesting a curved surface. > > "Imprecision" has no business in mathematics; as to > you suggesting "a > curved surface", it seems plain to me that you have > simply no idea or > notion what "curved surface" means in mathematics, > and instead > continue to insist on using your own personal > quasi-definitions and > notions. > > You are not communicating, you are engaging in an > extended monologue. > > > -- > Arturo Magidin > This comment about a curved surface is as though there is an objective reality of a math concept. All concepts in mathematics are creations of the human mind. The brain is structured and functions in a certain way and its products are structured in a way that the brain naturally can work with. Professionals come to believe that this figment of imagination is a real object, and it seems that it is necessary for the philosophy of science to remind them otherwise. When my brain has within a kinesthetic spatial area an image of a curved surface, the brain knows what it has. To translate this image into words or symbols is a task the the human sometimes has difficulty with when it is a new construction. When you say I do not know what a curved surface is within mathematics, I say I have difficulty putting this unique construction into words, but my brain knows, and it is presumptuous of you to say otherwise. When you say I am having a two person conversation with myself, I agree. In a certain approach in psychology, there is the concept of the inner community. I am not getting much help in getting an outer dialogue.
From: Tonico on 22 May 2010 10:23 On May 22, 4:01 pm, DRMARJOHN <MJOHN...(a)AOL.COM> wrote: > > On May 21, 11:54 pm, DRMARJOHN <MJOHN...(a)AOL.COM> > > wrote: > > > > There is a simple illustration to FLT.... > > > > There is the maxim Parallel lines converge at > > infinity.... > > > > For FLT, when A^n + B^n = 1, (0<R<1) all real > > numbers between 0 and 1... > > > There are two sets of solutions.... > > > There is a first A^n & B^n above and below .5.... > > > There is a second A^n & B^n above and below .5.... > > > There is a third A^n & B^n above and below .5.... > > > ...There is an Nth A^n & B^n above and below > > .5.... > > > There are an infinite # of such pairs.... > > > > The second repeats the first set,.... > > > > Irrational roots have a Terminus at an infinite > > point.... > > > > For the beginning pair, the first solution of .5 + > > .5 = 1.... > > > > The character of the irrational base enables > > success.... > > > > Only irrational roots give solutions.... > > > > Martin Johnson. > > > > It astounds me that the maxim parallel lines > > converge at infinity.... > > > Nowhere do you make any distinction between n = 3, > > say, and n = 2. > > Your argument seems t apply equally well to a^3 + b^3 > > = 1 and to > > a^2 + b^2 = 1. > > So how do you account for (.6)^2 + (.8)^2 = 1? > > Or (.384615384615384615,,,)^2 + > > (.923076923076923076...)^2 = 1? > > (that's (5/13)^2 + (12/13)^2 = 1). > > -- > > GM > > The question of FLT is posed for n=3 and more. > N of 3 is exponential. X^2 is straight line. That X^2 x X^2 = X^4 only gives the appearence that X^2 is in the same "family" as X^3. Humans created these conventions and the appearence of similarity does not make them the same. When you, a mathematician ask this kind of question, I, a novice, have to answer from a naive perspective, I have to figure it out in my own way, which may not have the language you are used to. I learned abou 3, 4, 5 in the illustration of a right triangle, with a visual flat plane. That 25 squares just does not expand into the three dimensional. In the examples I use: for .9^3, .9 x .9 = .81, .9 x .81 = .729. please bear with my primative illustrations. The square root of .729 is not .81. I say this because X^3 is X x X x X, ** I thought you said this because certainly 0.81 is NOT even close to the square root of 0.729, which is approx. 0.853814...what does x^3 and stuff have to with all this? Tonio and in the expansion of X to X^3 there is this intermediary step of X x X. The convention of one looks similar to the other, but an intermediary step does not -- well, like, One swallow does not make a spring. > I sincerely appreciate your offering this question. You take with some seriousness my naive effort; my effort includes years of struggle and reading many books (almost all before 2003, when I put aside my work -- I have forgotten most of what I read, one reason my language is primitive.) I have crunched numbers for many hours in the past month -- so this latest approach is based on real numbers. I do not speculate from detached ideas. > > Martin Johnson-
From: J. Clarke on 22 May 2010 10:14 On 5/22/2010 9:01 AM, DRMARJOHN wrote: >> On May 21, 11:54 pm, DRMARJOHN<MJOHN...(a)AOL.COM> >> wrote: >> >>> There is a simple illustration to FLT.... >>> >>> There is the maxim Parallel lines converge at >> infinity.... >>> >>> For FLT, when A^n + B^n = 1, (0<R<1) all real >> numbers between 0 and 1... >>> There are two sets of solutions.... >>> There is a first A^n& B^n above and below .5.... >>> There is a second A^n& B^n above and below .5.... >>> There is a third A^n& B^n above and below .5.... >>> ...There is an Nth A^n& B^n above and below >> .5.... >>> There are an infinite # of such pairs.... >>> >>> The second repeats the first set,.... >>> >>> Irrational roots have a Terminus at an infinite >> point.... >>> >>> For the beginning pair, the first solution of .5 + >> .5 = 1.... >>> >>> The character of the irrational base enables >> success.... >>> >>> Only irrational roots give solutions.... >>> >>> Martin Johnson. >>> >>> It astounds me that the maxim parallel lines >> converge at infinity.... >> >> Nowhere do you make any distinction between n = 3, >> say, and n = 2. >> Your argument seems t apply equally well to a^3 + b^3 >> = 1 and to >> a^2 + b^2 = 1. >> So how do you account for (.6)^2 + (.8)^2 = 1? >> Or (.384615384615384615,,,)^2 + >> (.923076923076923076...)^2 = 1? >> (that's (5/13)^2 + (12/13)^2 = 1). >> -- >> GM >> > > The question of FLT is posed for n=3 and more. > N of 3 is exponential. X^2 is straight line. Perhaps so in your universe in which parallel lines meet. > That X^2 x X^2 = X^4 only gives the appearence that X^2 is in the same "family" as X^3. Humans created these conventions and the appearence of similarity does not make them the same. When you, a mathematician ask this kind of question, I, a novice, have to answer from a naive perspective, I have to figure it out in my own way, which may not have the language you are used to. I learned abou 3, 4, 5 in the illustration of a right triangle, with a visual flat plane. That 25 squares just does not expand into the three dimensional. In the examples I use: for .9^3, .9 x .9 = .81, .9 x .81 = .729. please bear with my primative illustrations. The square root of .729 is not .81. I say this because X^3 is X x X x X, and in the expansion of X to X^3 there is this intermediary step of X x X. The convention of one looks similar to the other, but an intermediary step does not -- well, like, One swallow does not make a spring. > I sincerely appreciate your offering this question. You take with some seriousness my naive effort; my effort includes years of struggle and reading many books (almost all before 2003, when I put aside my work -- I have forgotten most of what I read, one reason my language is primitive.) I have crunched numbers for many hours in the past month -- so this latest approach is based on real numbers. I do not speculate from detached ideas. It's clear that you need a math refresher if you are going to make any progress at all. Recognize that it has been a _long_ time since your math courses and that you have probably forgotten some basic things. You're making statements that are flat out _wrong_ and then going on to come up with elaborate theories based on those statements. You need to get some basics down. You might want to start with the Schaums Outline of "Precalculus Mathematics"--it covers a lot of territory quickly.
From: J. Clarke on 22 May 2010 10:48
On 5/22/2010 9:29 AM, DRMARJOHN wrote: >>> >>> In my imprecise way I suggesting a curved surface. >> >> "Imprecision" has no business in mathematics; as to >> you suggesting "a >> curved surface", it seems plain to me that you have >> simply no idea or >> notion what "curved surface" means in mathematics, >> and instead >> continue to insist on using your own personal >> quasi-definitions and >> notions. >> >> You are not communicating, you are engaging in an >> extended monologue. >> >>> -- >> Arturo Magidin >> > This comment about a curved surface is as though there is an objective reality of a math concept. No, it is as though there is an accepted definition of "curvature" in mathematics and any surface that lacks that property is not curved. If you are going to redefine "curvature" to suit your own purpose that is fine, but you need to state explicitly that you are doing so, and state your definition, and give some justification for it. > All concepts in mathematics are creations of the human mind. Which has no relevance. Mathematics has certain rules and procedures. If you play by those rules you're doing mathematics. If you refuse to play by those rules then you are doing something else. > The brain is structured and functions in a certain way and its products are structured in a way that the brain naturally can work with. Which again has no relevance. We are not talking about brain structure, we are talking about a specific mathematical theorem. If you think that brain structure and function have relevance to a proof of that theorem, the burden on you is to show that that is the case. > Professionals come to believe that this figment of imagination is a real object, and it seems that it is necessary for the philosophy of science to remind them otherwise. You don't want to go there. Really, you don't. > When my brain has within a kinesthetic spatial area an image of a curved surface, the brain knows what it has. That's nice, but if you can't define it then you can't discuss it mathematically. > To translate this image into words or symbols is a task the the human sometimes has difficulty with when it is a new construction. And yet the procedures for doing so are well established in mathematics. > When you say I do not know what a curved surface is within mathematics, I say I have difficulty putting this unique construction into words, but my brain knows, and it is presumptuous of you to say otherwise. Well, there anybody who has completed freshman calculus has an advantage over you, because he can define curvature in words and symbolically. > When you say I am having a two person conversation with myself, I agree. In a certain approach in psychology, there is the concept of the inner community. I am not getting much help in getting an outer dialogue. That is because you are paying very little attention to what you are being told. If a mathematician told you that sociopaths can be cured by giving them two aspirin and having them call you in the morning how would you respond? |