Fermat's Last Theorem simple proof impossible?
in [Math]
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From: DRMARJOHN on 6 May 2010 03:25 If I say .9 is a root, and I take it to the 3rd power, I get .729. The cube root of .9 is .729. .99 to the third power is .970299. If I say .999999 is a root and I take it to any power, I get a rational number. At any place I truncate the irratiional root, I get a real number. If this is at the Nth position, then this number to the Nth power is a rational number. There has to be someone who sees any problem from a different perspective. You get in a negative attitude when you ask, do you think you are smarter than anyone else, that may block you from considering what I am presenting. I respect you for attempting to have a conversastion with this naive person. (by the way, I can not find on my laptop the symbol like >.)I woke up thinking of two things I wanted to say to you. They are in the submission I made a few minutes ago. I saw someoneelses answer before I saw yours. With all due respect, thank you. See my answers to my previous submission
From: J. Clarke on 6 May 2010 08:27 On 5/6/2010 7:25 AM, DRMARJOHN wrote: > If I say .9 is a root, and I take it to the 3rd power, I get .729. The cube root of .9 is .729. No, the cube of .9 is .729. 0.9 is the cube root of .729. > .99 to the third power is .970299. If I say .999999 is a root and I take it to any power, I get a rational number. If you say it's the Queen of the May and take it to any power you still get a rational number. Calling something a root doesn't make it a root unless you want to redefine the term "root" in which case you need to state your definition of "root" and explain why you are redefining it. > At any place I truncate the irratiional root, I get a real number. If you do't truncate it you still get a real number. > If this is at the Nth position, then this number to the Nth power is a rational number. This is true, but Fermat's Last Theorem is not about rational approximations. > There has to be someone who sees any problem from a different perspective. The perspective I get is that you really need to find a good calculus text and read up on the concept of limits, because you seem to be trying to reinvent that particular wheel. > You get in a negative attitude when you ask, do you think you are smarter than anyone else, that may block you from considering what I am presenting. I'm considering it but I don't see where you're going to make any progress with it. > I respect you for attempting to have a conversastion with this naive person. > (by the way, I can not find on my laptop the symbol like>.) The ">" symbol is normally the "SHIFT-." (that's the shift key and the period) on US English keyboards. If you're using a keyboard layout for another language I dunno. > I woke up thinking of two things I wanted to say to you. They are in the submission I made a few > minutes ago. I saw someoneelses answer before I saw yours. With all > due respect, thank you. > See my answers to my previous submission
From: Gerry Myerson on 7 May 2010 02:16 In article <596411544.81142.1273143394318.JavaMail.root(a)gallium.mathforum.org>, DRMARJOHN <MJOHNMAR(a)AOL.COM> wrote: > Thank you for your comments. I understand about my naive vocabulary is > different tnan yours. It's not just different, it's vastly inferior. It fails to communicate, which is what mathematics ought to do. > But you understand my last entry- I also meant that > there are an infinite number by letting N go to infinity. I don't know what you are talking about, since you have snipped anything that could have explained it. > I have two other questions, and my answers, that I think my vocabulary will > convey what I mean: > > First,an answer to your question about N_2 vs N_3. There is a structural > difference betwen the realm of FLT and that of square roots. The change > between A and A_2 is in a straight line. What is A? What is A_2? > The change between A and A_2 and > A_3 is what can be called a curve. The difference between .9 and .9_2 What in heaven's name is .9_2? Numbers don't have subscripts - there's only one .9, you know. > and .9_3 is .09, then .081. If you graph .9_10 (.9 to the 10th power) > and you connect the dots I daresay you will draw a curve. My question > is, has anyone asked this naive question and seen the high school > math answer? What naive question? I think a lot of people have asked what the graph of y = (.9)^x looks like, and everyone who has passed high school mathematics has worked out the answer, if that's what you're asking. But there's nothing special about the point on the curve corresponding to x = 2. > My second question: has anyone presented the naive observation that the realm > of FLT is different than other equations, in that in FLT an odd number can > only be multiplied by an odd number, an even number by an even number. How many equations are you familiar with? And again, how is the n = 2 case any different? a^2 + b^2 = c^2, we only multiply a number by itself, so an odd only by an odd, an even only by an even. > If you graph .8_10 below .9_10 you will see that these curves diverge, Wait a second, I thought you said .8_10 was your way of writing what the rest of the world writes as (.8)^(10), the 10th power of .8; so you're talking about two numbers; what curves? > that .8 changes faster than .9. In my experience, .8 doesn't change at all. It's one of those things you can count on in an ever-changing world, that .8 will always be exactly where it was the last time you used it. Wait a sec - I think you mean y = (.8)^x decreases faster than y = (.9)^x. Well, this is something we can check, with calculus, and it turns out that you are wrong. > If you imagine an irrational curve What is an irrational curve? Is it a curve drawn by an irrational person? > between these two. at the nth > position, the lower curve will be further away. Do it this way: plot > .7_10. At A_N. the distance between .7_N and .8_N is more than the > distance between .8_10 and .9_N. Finally, something with mathematical content. So you're saying that, for n = 2, 3, ..., (.8)^n - (.7)^n > (.9)^n - (.8)^n, right? I suggest you let n = 3, and see what happens. There is a reason mathematicians talk the way we do - it helps us avoid stupid mistakes. > In my mind I think of these as structural differences. It is these factors > that lead me to see FLT the way I do. Then maybe it's time to abandon these factors and look for some that make sense. > I also plot the hypothetical curves > from A to A_N, rather than view all the possibilities for any one exponent. I don't know what this means. > I would suggest that once Fermat presented a proof for the exponent > 4, all followed him, and ran into problems. What makes you think everybody followed Fermat? Have you read even one proof put forward by a later mathematician? Have you even read and understood Fermat'sproof for n = 4? -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: DRMARJOHN on 7 May 2010 07:35 > In article > <596411544.81142.1273143394318.JavaMail.root(a)gallium.m > athforum.org>, > DRMARJOHN <MJOHNMAR(a)AOL.COM> wrote > > > Thank you for your comments. I understand about my > naive vocabulary is > > different tnan yours. > > It's not just different, it's vastly inferior. It > fails to communicate, > which is what mathematics ought to do. > > > But you understand my last entry- I also meant that > > > there are an infinite number by letting N go to > infinity. > > I don't know what you are talking about, since you > have snipped > anything that could have explained it. > > > I have two other questions, and my answers, that I > think my vocabulary will > > convey what I mean: > > > > First,an answer to your question about N_2 vs N_3. > There is a structural > > difference betwen the realm of FLT and that of > square roots. The change > > between A and A_2 is in a straight line. > > What is A? What is A_2? > > > The change between A and A_2 and > > A_3 is what can be called a curve. The difference > between .9 and .9_2 > > What in heaven's name is .9_2? Numbers don't have > subscripts - there's > only one .9, you know. > > > and .9_3 is .09, then .081. If you graph .9_10 (.9 > to the 10th power) > > and you connect the dots I daresay you will draw a > curve. My question > > is, has anyone asked this naive question and seen > the high school > > math answer? > > What naive question? > > I think a lot of people have asked what the graph of > y = (.9)^x > looks like, and everyone who has passed high school > mathematics I am not asking if they have looked at that curve--I am asking if have they applied that curve to the progression from A(3) (A cube -- I do not have that carrot turned vertical) to A(n) (the Nth power) which is different than looking at all the cases of FLT at the 3rd power, then at a separate time, the 4th power, etc. > has worked o the answer, if that's what you're > asking. But there's > nothing special about the point on the curve > corresponding to x = 2. > > > My second question: has anyone presented the naive > observation that the realm > > of FLT is different than other equations, in that > in FLT an odd number can > > only be multiplied by an odd number, an even number > by an even number. > > How many equations are you familiar with? And again, > how is the > n = 2 case any different? a^2 + b^2 = c^2, we only > multiply a number > by itself, so an odd only by an odd, an even only by > an even. > > > If you graph .8_10 below .9_10 you will see that > these curves diverge, > > Wait a second, I thought you said .8_10 was your way > of writing what > the rest of the world writes as (.8)^(10), the 10th > power of .8; > so you're talking about two numbers; what curves? > > > that .8 changes faster than .9. > that the curve of .8 changes faster than the curve of .9 > In my experience, .8 doesn't change at all. It's one > of those things > you can count on in an ever-changing world, that .8 > will always be > exactly where it was the last time you used it. > > Wait a sec - I think you mean y = (.8)^x decreases > faster than > y = (.9)^x. Well, this is something we can check, > with calculus, > and it turns out that you are wrong. > such a simple task, and your turn to calculus? Do mathematicians always look to the more complicated? 9 x.9= .9 x (1-.1)= .9 -.09. the .09 is the amount of decrease. for .9(3): .81 x .01 = .081 8 x (1-.2)= .8 -.16, .16 is the amount of decrease. for then .74 x .2 =.148. Compare the rate of decrease: .09 and .081 to .16 and .148. Is the rate of change for .8(n) faster than the rate of change for .9(n)? > > If you imagine an irrational curve > > What is an irrational curve? Is it a curve drawn by > an irrational person? > > > between these two. at the nth > > position, the lower curve will be further away. Do > it this way: plot > > .7_10. At A_N. the distance between .7_N and .8_N > is more than the > > distance between .8_10 and .9_N. > > Finally, something with mathematical content. So > you're saying that, > for n = 2, 3, ..., (.8)^n - (.7)^n > (.9)^n - (.8)^n, > right? I suggest > you let n = 3, and see what happens. > > There is a reason mathematicians talk the way we do - > it helps us > avoid stupid mistakes. > > > In my mind I think of these as structural > differences. It is these factors > > that lead me to see FLT the way I do. > > Then maybe it's time to abandon these factors and > look for some > that make sense. > > > I also plot the hypothetical curves > > from A to A_N, rather than view all the > possibilities for any one exponent. > > I don't know what this means. > > > I would suggest that once Fermat presented a proof > for the exponent > > 4, all followed him, and ran into problems. > > What makes you think everybody followed Fermat? Have > you read > even one proof put forward by a later mathematician? > Have you even > read and understood Fermat'sproof for n = 4? > > It was many years ago--I read books that included Fermat's proof--I thought I understood it. And descriptions of those who followed him. I meant followed by always looking for more esoteric means--not all, almost all. > Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for > email)
From: DRMARJOHN on 7 May 2010 07:44
> > May I begin again? > > For .5000 + .5000 = 1.000 (An + Bn = Cn = 1.000): > > Consider the roots of .5000 from the exponent 3 to > the exponent N. > > Why start with the exponent 3? What happens if you > start with 2 instead? > If everything you do for 3 works for 2, then anything > you come up with > for x^3 + y^3 = z^3 will also apply to x^2 + y^2 = > z^2, which ought > to tell you something. > > > As the > > roots approach infinity, > > I guess you mean, as you take n-th roots with n > approaching infinity. > > > A approaches 1.000. As it approaches infinity, > > consider a pair of rational roots just above and > just below the irrational > > root of .5000. Call this An and Bn. At N-1 root, > there are also a pair of > > rational roots. At N-2, at N-3...descending to the > third root, there are > > pairs of rational A's and B's. This contains all > the possible A's and B's. > > Note that this approach does not consider all the > domain of the third power, > > instead it goes from the exponent 3 to the exponent > N. The question, is this > > all-possible-As-and-Bs a finite quantity or an > infinite quanity? > > If you fix N, and take just one rational number > either side of > the n-th root of 1/2 for each n, then you're talking > about > a finite quantity of A_n and B_n. But if you let N go > to infinity, > or if for any particular n you look at all the pairs > you can get > by truncating the n-th root at different numbers of > decimal places, > then you're talking about inifnitely many A_n and > B_n. > You understand my last entry- I also meant that > there are an infinite number by letting N go to > infinity. > -- > Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for > email) |