Fermat's Last Theorem CORRECTION
Kenneth Collins
k.p.collins at worldnet.att.net
Mon Jun 10 06:43:19 EST 2002
those who are feeling like the duck in the Yogi-Berra's-getting-a-haircut
insurance commercial, your nervous systems serve you well.
sorry.
CORRECTION of what i posted is given below.
Kenneth Collins wrote in message
<1Q_M8.29841$LC3.2283899 at bgtnsc04-news.ops.worldnet.att.net>...
>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.
the above paragraph is B.S.
the term on the right, while being a Square, numerically, as well as
coincidentially, Geometrically, is the hypotenuse of the right triangle with
sides x and y. this's where, everything gets precisely-defined, for all n,
all the way to infinity, via Pythagorean incommensurability.
what i meant to say is that the hypotenuse of the left and right hand
Squares is exactly the same length, and this, too, is infinitely-precise
with respect to n=2.
all that's necessary for the Proof is this infinite-precision and
integer-discreteness.
>
>therefore, if n=2 works within this precise-to-infinity Geometry, no n>2
can
>work.
>
>all any n>2 can do is ge[t] 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% [energy-flow] Geometry.
>
>K. P. Collins
i know i should proofread stuff before i 'send' it, but i can't get my
'caring' geared-up sufficiently.
it's just as easy to 'wing-it', and pick-up-the-pieces, if need be.
results, for me, are the same, anyway.
"Yeah, but if you got your foot out of your mouth =before= you tried to say
something, then maybe someone would listen to you."
folks're 'listening'. don't know how many.
the stuff is gettin'-out-there. to at least a few.
i'm just "running on empty", but gotta keep runnin'.
"wingin'-it", or whatever else can get-me-through what needs to be done.
still, it 'hurts' to get something Beautiful all-screwed-up, especially when
i was trying to make the larger 'point' about there being an inner-edge that
needs just as much sharpening as the familiar outer-edge of Knowledge.
Humble Apologies for, once again, being,
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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