Fermat's Last Theorem CLARIFICATION
Kenneth Collins
k.p.collins at worldnet.att.net
Mon Jun 10 05:03:41 EST 2002
still don't get it?
the way i did it was [as usual], to just See it, in its inherent Geometry.
when n=2, x^n is a Square, y^n is a Square, z^n is a Square, each Square
infinitely-precise.
merge the two terms on the left side, via Addition, yielding an
infinitely-precise Square that's exactly-similar to the infinitely-precise
Square on the right.
"A Square is a Square."
and since the term on the right is also the diagonal of either of the
exactly-similar Square, which is also the hypotenuse of either of the two
right triangles that comprise each of the exactly-similar Squares,
Pythagorean incommensurability "seals" everything, all the way to infinity.
therefore, if n=2 works within this precise-to-infinity Geometry, no n>2 can
work.
all any n>2 can do is ger closer and closer, but never satisfy Equality.
all n>2 behave Asymptotically.
QED.
all the folks who thought it's Simple were Correct.
it's as Albert Szent-Gyorgyi said.
the 'difficulty' arose in folks' starting to 'figure' beyond the fundamental
form of Fermat's Last Theorem.
it's my first 'rule' of problem-solving: always lay the foundation on the
bedrock-stuff.
why it's so often 'skipped' is be-cause it's 'fashionable' to begin to
search 'out at the edges' of what's already 'known'.
problem with that is that it 'takes it on' 'faith' that what's already
'known' is actually "Known" [when is usually isn't].
so-called 'quantum mechanics' suffers the same 'difficulty'.
so does 'molecular' Neuroscience, which, including its Chemistry, is, as
i've discussed, 100% Geometry.
K. P. Collins
Kenneth Collins wrote in message ...
>CLARIFICATION:
>
>Kenneth Collins wrote in message
><93zL8.23329$LC3.1751601 at bgtnsc04-news.ops.worldnet.att.net>...
>>The Proof of FLT is quite simple.
>>
>>"Among Fermat's cherished Latin translations of ancient texts was a book
>>called _Arithmetica_, written by the Greek mathematician Diophantus who
>>lived in the third century A.D. Around 1627, Fermat wrote in Latin in the
>>margin of his Diophantus, next to a problem on breaking down a squared
>>number into two squares:
>>
>>'On the other hand, it is impossible to separate a cube into two cubes, or
>a
>>byquadrate into two biquadrates, or generally any power except a square
>into
>>two powers with the same exponent. I have discovered a truly marvelous
>proof
>>of this, which, however, the margin is not large enough to contain.'"
>>[_Fermat's Last Theorem_, by A. D. Aczel, [c] 1996, ISBN0-385-31946-0, p9]
>>
>>Fermat's Last Theorem: x^n + y^n = z^n has no whole number solution where
n
>>is greater than 2." [ibid, pviii.]
>>
>>1. when n=2, the equation restates the Pythagorean Theorem, in which z^2
>>forms the hypotenuse of a right triangle.
>>
>>2. the Pythagoreans verified that, when n>2, the hypotenuse of a right
>>triangle is Incommensurable. there exist no unit measures other than 1 and
>>2, all the way out to infinity, that can measure the lengths sides of the
>>triangle and the length of its hypotenuse.
>
>sorry, 2. is not what i meant to state (i don't even know if it's True :-)
>
>it's the ratio of side to hypotenuse that's incommensurate.
>
>what's important is that this property defines the Fermat equation in an
>infinitely-precise way.
>
>>
>>3. integers are discrete.
>>
>>4. it follows from integer-discreteness and infinitely-rigorous
Pythagorean
>>incommensurability, that if n=2 works, then no integer >2 can work in the
>>Fermat equation. [1 'works' because any number raised to the 1-power is
>just
>>the original number, so the equation becomes non-exponent-ed [x + y = z],
>>which isn't the equation of FLT.]
>>
>>i believe that this simple Proof is a good candidate for what was in
>>Fermat's mind when he wrote the problem in the margin of the book he was
>>reading.
>>
>>i'd stated it [using other words; "a square is a square..."]] before
>reading
>>the Author's article. After reading the article, i wrote a program that
did
>>a numerical analysis. the program verified that all integers >2 behave
>>asymptotically re. the Fermat equation. this asymptotic stuff reiterates
>>integer-discreteness.
>
>...with specific respect to the Fermat equation.
>
>a Square is an infinitely-precise entity.
>
>when n=2, the Fermat equation describes a Square.
>
>if it's infinitely-precise, and the integers are discrete, then it cannot
be
>reproduced for n>2.
>
>it is. they are.
>
>why all this 'hubbub?
>
>"because it's there."
>
>ken
>
>>
>>other matter: if folks want to get a handle on all the data that's been
>>'slipping-through' [FBI, CIA, NSA], its meaning undetected, and
>>unintegrated. i'll be happy to show [those folks] how to build a system
>that
>>can do the Integration and present its integrated-meaning in a way that's
>>accessible in 'real-time' [with respect to putting the info in].
>>[...]
>
>
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