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December 16th, 2016, 09:22 PM   #91
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There are now some interesting concerning for thos understand what I did:

1) Better investigating we can distinguish in:

(1) $f:\mathbb{N} \to \mathbb{N}$

a) In the case we start from an Integer and we arrive to an Integer Result, but we have no restrictions on how the transformation happens.

b) In a most strictly definition, for what is necessary to recall the signify of Unit Tessel (be it a segment, a flat shape or an hyperdimensional tessel, where the "function" strictly work with re-arrangements of such Units.

Once we understood that, it's clear Fermat's case works with Power of integers JUST, so I show thant to Power's property, we can use the most strictly definition of the (1), so we have the very easy and intuitive lever to close the elegant proof: we can just re-arrange Unit Tessel or integer/Rational Gnomon Tessels, so it's enough to prove that the trasformation imply to go Irrational (so via limit) to prove Fermat is right. And it's nice because we have a more clear vision of what the proper "infinite descent" means.

Once again, I repeat, Beal follow as a much less easy problem, once we understand that in the case (b) a common solution has a common $Base$, because all 3 sets must be a collection of Units or Gnomons, so since Intereg and Rational Powers are always Built on a Abscissa starting from the Unit, to a certain value we know as $Base$ then we don't need to search far from there, we have just to find the condition that will balance the heights of the gomons that, as told, can be ordered in just one rising way.

Linearization process, so the reduction of the problem to a Linear Gnomons, I several Time show here, let think become very easy.

Are my words blown in the wind, or someone someone is listening?

I won't make theorems, I simply play with well working gears...

Last edited by complicatemodulus; December 16th, 2016 at 09:27 PM.
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December 19th, 2016, 06:51 AM   #92
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It's clear to someone the difference in the case $n=2$ (linear derivate) and the case $n>2$ what my Step Sum (so the scaling) square ?

It's clear that the curve change rising K, becoming $y'=nX^n$ just at the limit ?
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December 19th, 2016, 08:01 AM   #93
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Here going Rational K=4:



Here the table of the gnomons, all are Base 0,25 Height as in the last colum:



Rising K, no way to rise the given Area: A^3+B^3 = 5^3+6^3 = 341, we still rest bellow...

Clear while several months ago I post Flt is a collection of Dedekind sections ???

ciao
Stefano

Last edited by complicatemodulus; December 19th, 2016 at 08:51 AM.
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December 19th, 2016, 08:57 AM   #94
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There's been ample time for anyone to respond. Topic closed (this is not a blogging site).
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