Fermat's Last Theorem simple proof impossible?
in [Math]
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From: Arturo Magidin on 7 May 2010 15:58 On May 7, 2:35 pm, DRMARJOHN <MJOHN...(a)AOL.COM> wrote: > > On May 7, 10:35 am, DRMARJOHN <MJOHN...(a)AOL.COM> > > wrote: > > > > 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. > > > The "carat" (not carrot) symbol, ^, is usually > > located above one of > > the numerical keys. But if you do not have it, then > > "x(n)" with the > > explanation is a good compromise. > > > That said: to me, at least, what you are saying is > > still rather > > unintelligible. What do you mean by "curve"? (To me, > > a curve is either > > a continuous map from an interval to n-dimensional > > real (or complex) > > space; or a one-dimensional algebraic > > variety/scheme). What does it > > mean to "apply" a curve? What is "the progression > > from cube [...] to > > nth power"? What "progression"? > > > Now, the map a^x, with a fixed and x varying, is also > > well-known, well- > > understood, and much studied. Of course, between x=3 > > and x=4 there are > > a lot of values: there is no "jump" from one to the > > other. That's the > > closest I can come to whatever the heck it is you > > think you are > > saying. > > May I have a referance to "the map of a^x? It's called an "exponential function" or "exponential map". All of my calculus textbooks that include "early transcendentals" include discussions of the exponential functions a^x, where a is a positive integer different from 1 > An example: > 99^5: .99, .9801, .970299, .96059601, .9509900499 This makes *NO SENSE WHATSOEVER* to me. I have no idea what it is you think this communicates, but to me it communicates absolutely nothing. > A curve is not correct. .999^5 changes by .000000999, which plotted looks more like a curve. can I use curve in quotes, saying what I mean? Again, the words, by themselves, I understand. But they that you've put them together is meaningless to me. I suspect that you are rather confused in your own mind about what it is you are trying to say, and this is further complicated by being confused as to how to express what you think, at any given time, that you wish to say. But, in any case, to me you are not actually saying anything intelligible. I find *unable* to make *any* sense out of anything you write. > Again, thank you. I will take several days off. You need more than a few days off. To make yourself understood at this point, you need to clarify in your own mind what it is you want to say, and then start from the beginning, very slowly. So far, what we have is (to quote "Cool Hand Luke") a failure to communicate. You seem to think that you are saying things with meaning, but I'm not finding any sense in what you are saying. -- Arturo Magidin
From: spudnik on 7 May 2010 16:19 I don't know what he was getting at, but 99x99=9801 etc. Fermat could have discovered p-adic integers, and p-adic numbers. thus: so, why do *you* believe that oil companies do not "like" the Kyoto Protocol and other capNtrade schemes ... even though several openly support them and GW ("Beyond Petroleum (TM)" e.g.) ?? thus: find Hipparchus' "lunes" proof of the pythagorean theorem -- if it was not the original proof -- and you'll see that circles are better fro areal mensuration; generalize to prove the spatial pythagorean theorems -- there are two of them -- and you'll see that, not only does second-powering have nothing in particular to with the tetragon, but also not with a two-dimensional object. thus: like I said, dimensional analysis is fine, and woe to he who ignores it, but it cannot be used ex post facto to remake a wave-form into a particle. surely, the wave can impart, at least, internal "momentum" to the atomic system that is tuned to absorb it. that is, whatever energy propogates through the *medium* of space, not a vacuum, is in its effect upon that medium just as waves in H2O. so, do not apply "momentum" to the wave, only as a formalism for the seemingly-aimed "photon" that was speared by the cone of your eye. so, you can use other, valid formlisms, like E=hf, or what ever. otherwise, you get absurdities like the EPR paradox, and simplistic statements about the photoelectrical effect. not to say that a total formalism of rocks o'light is not possible, and a gravity that is "pushed" by such-like, but it is probably at present "intractible," even as Huyghens wavelets are intractible, except for getting a concept of light, propogating. (photons are massless & cannot propogate at any speed, because they don't exist, is my feeling, even though they are the only "zero-D particle" that can "go at c.") as for wlym.com, folks who pretend to "do the math," should know what *mathematica* ("maths") is; if you "go" to wlym.com, and hit the Fermat button, and find the Geometrical Fragments pdf, you''ll find his reconstruction of Euclid's porisms, whis are quite elementary (and planar). lastly, here is a thought experiment: what are those little black & white paddle-wheels, tht rotate in the sunlight in clear globe?... since there is no actual vacuum in the globe, provide an *aerodynamical/thermal* explanation of the force, after waves of light have been absorbed by the black pigment in the vanes. thought of that, yesterday, after more of this chat. > Get rid of that [M] dimension in the photon equation thus: Moon could have supported life, a long time ago (i.e., smaller bodies have shorter lives), as is evidences by the remnants of plate tectonics (maria & highlands). > >http://www.meteorite.com/meteorite-gallery/meteorites-alpha_frame.htm thus: you call that, an explanation, "photons wedged apart by light rays?" an interesting relationship between two things that only exist as mathematics, both representing "rocks o'light!" thus: you are pretending to define "complex 4-vectors," but "real" 4-vectors are part of the gross and unfinished porgramme of Minkowski, to "spatialize" time, while it is quite obvious that the "time part" is not symmetrical with the spatial coordinates, either in 4-vectors or quaternions. anyway, bi-quaternions would be 8-dimensional or octonions. and, it is all obfuscation, trying to insist that a phase-space tells you what time really is; it's very useful for seeing patterns "in" time though, as in electronics (although, NB, electronics is mostly done in "1-1" complex phase-space, instead of quaternions, as it could be, for some reason .-) maybe, all you and polysignosis need to do, is work the math of quaternions ... that'll take me wome time, as well. (I mean, what is the difference in labeling a coordinate axis with a "different sign" and a different letter, whether or not negatives are even needed?) --Light: A History! http://wlym.com --Stop Waxman's #2 capNtrade rip-off (unless, you like gasoline at a dime per drop)
From: spudnik on 8 May 2010 17:22 to reiterate, for the sake of Obispo, above, Fermat had to prove the very special case, n=4, because his proof only applied to prime exponents, excepting two (plus the lemma on multiples of prime exponents). thus: yeah, OK; so, what is the difference between "energy" and "aether?..." what is the shape of the wave of light? > Aether is matter times the second power of the speed of light. thus: spatially, there are "mutually inscribed tetrahedra," meaning that the vertices of one lie on the faces of the other, and vise versa. thus: the formalism of relativity isn't needed, if one does not presume that Pascal's vacuum was perfect (and still is) a la "Newtonian optics" or ray-tracing, and the calculus-launch problemma of the brachistochrone. thus: how about this: show us that your theory agrees with Sophie Germaine; then, tackle the remaining primes. thus: NB, Lanczos used quaternions in _Variational Mechanics_ for special relativity, and it's just "real time" and "three ('imaginary') axes of space;" but, this is just the original "vectors." compare Lanczos' biquaternions with the "Cayley-Dickerson doubling" procedure, to go from real to complex to quaternion to octonion. "wroldlines" are just the crappola in Minkowski's "pants," totally obfuscatory outside of a formalism -- time is not a dimension; time is awareness & mensurability (of dimensionality !-) thus: try a search on Gauss & Ceres. or "go" to wlym.com. > This problem and its solution are found in a paper by Ceplecha, 1987, thus: the problem appears to be, "some observers measure the angle to the marker, relative to the other observers," which would not give you the distance *on a plane*, because of similar trigona. Gauss meaasured the curvature of Earth with his theodolite *and* a chain measure of distance (working for France in Alsace-Lorraine, triangulatin' that contested area .-) thus: notice that no-one bothered with the "proofs" that I've seen, and the statute of limitation is out on that, but, anyway, I think it must have been Scalia, not Kennedy, who changed his little, oligarchical "Federalist Society" mind. thus: sorry; I guess, it was Scalia who'd "mooted" a yea on WS-is-WS, but later came to d'Earl d'O. ... unless it was Breyer, as I may have read in an article about his retirement. > I know of at least three "proofs" that WS was WS, but > I recently found a text that really '"makes the case," > once and for all (but the Oxfordians, Rhodesian Scholars, and > others brainwashed by British Liberal Free Trade, > capNtrade e.g.). > what ever it says, Shapiro's last book is just a polemic; > his real "proof" is _1599_; > the fans of de Vere are hopelessly stuck-up -- > especially if they went to Harry Potter PS#1. > http://www.google.com/url?sa=D&q=http://entertainment.timesonline.co.... --Light: A History! http://wlym.com --Waxman's capNtrade#2 [*]: "Let the arbitrageurs raise the cost of your energy as much as They can ?!?" * His first such bill was in '91 under HW on NOx & SO2 viz acid rain; so?
From: Gerry Myerson on 9 May 2010 19:23 In article <183738170.88978.1273246578253.JavaMail.root(a)gallium.mathforum.org>, DRMARJOHN <MJOHNMAR(a)AOL.COM> wrote: > > 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)? So, if something is true for the first three cases, it's true for all cases? If you had kept going, you would have found that somewhere around the 8th power, the change in .9-to-the-n is, as I claimed, bigger than the change in .8-to-the-n (see - you don't need a caret symbol to write intelligible mathematics). Mathematicians may or may not always look to the more complicated, but they definitely prefer techniques that give the right answers to techniques that don't. > > > 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. I notice you had nothing to say about this. No one makes progress in mathematics without integrity. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: DRMARJOHN on 14 May 2010 09:40
> > A^6 + B^6 = 1 > > A = .891 B = .890 > A^2 = .793881 B^2 = .792100 > A^3 = .707347971 B^3 = .704969000 > A^4 = .630247042161 B^4 = .62742241000 > A^5 = .561550114565451 B^5 = .55840594490000 > A^6 = .500341152097816841 B^6 = .496981290961000000 > > A^6 + B^6 = .997322442958816841 > > Between A & B, between .891 and .890, is an > irrational number, .890898718... > This irrational number is the 6th root of .5000. This > illustrates the statement that a pair of rational > numbers, the A & B, are above and below an irrational > root. The .891 is > .89089..., the .890 is< .89089... > . The A ends in 1 at the third decimal, the B ends in > a 0 at the 3rd decimal; they are one digit apart. The > rational roots are minutely different than the > irrational root. A ends in an odd number, therefore > A^6 is also an odd number. B is an even number, > therefore B^6 is an even number. If .8909 and .8908 > were used, the 9 at the fourth decimal of A would > be 1 at A^6. For B, the 8 (of the fourth decimal > place), would be 4 at B^6. Again the odd 1 of A^ 6 > and the even 4 at B^6 add to form an odd number, > which cannot be the last digit of 1.000. That A^6 + > B^6 are not close to 1.000 is beside the point. If A > and B were forms of the irrational root truncated at > the 100th decimal, then A^6 + B^6 may nearly equal > 1.000. It would be very rare that there is only a > difference of 1 at the last decimal. The assertion is > that it can never be a better fit than one because > A^n + B^n always ends in an odd digit. The abstract > statement is that the pair surrounding any irrational > root will always be different by one at the last > decimal, one odd and one even. These statements and > this and this illustration are only the beginning of > this discourse about essential mathematical process > underlying FLT. The purpose is not to find a proof, > but only to the rules of reveal how the rules apply > to FLT. What may be original may be a different way > of organizing material. Martin Johnson > > > C^n/2 + C^n/2 = C^n > C and C^n is the complete set of whole numbers above > 0. > C^n/2C^n + C^n/2C^n = C^n/C^n . C and C^n still is > the complete set of whole numbers above 0. Then 1/2 > +1/2 = 1 still represent the complete set of whole > e numbers above 0, but in fraction or decimal form, > with decimals between 0 and 1 ( 0<C^n<1). A^n and B^n > will be the complete set of rational numbers between > 0 and 1. Therefore when A^n = B^n = .5000, .5000 > represents any of the complete sets of positive whole > rational numbers above 0. All Nth roots of .5000 are > the complete set of positive irrational roots between > .5000 and 1.000, an infinite set. There is someone who has been working with the to explore this illustration. May I make a comment as a psychologist? Our brain contains a spatial imagery that is not a visual imagery, but like a kinaesthetic imagery. My experience of an insight after struggling with numbers is of a sudden shift in this projection screen. Then I was aware of a different perspective on the problem. If you keep working, you see a question, and you keep to it you may find an answer. I've been waiting for someone to point to a place that needs revision. If you do not find an answer, I have one. In this approach I've suggested, one can visualize two types of curved surfaces. If the y-axis is 0 to 1.00, and the x-axis the sequence of A^n and B^n to the Nth power, e.g., .5^2, .5^3, .5^4...5^N. The other has the y-axis the roots, i.e., all the possible A and B,first A, then A^2, A^3 when the root is the A^n to the 3rd power. For the 6th power of >918385902... that squared is .8427..., to the 3rd power is .7736..., to the 6th power, 6.000. There an infinite number of this other type of curved surface. Martin Johnson |