Re: Fermat's last theorem (New)
From: Jim Ferry (corklebath_at_hotmail.com)
Date: 09/30/04
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Date: 30 Sep 2004 08:46:05 -0700
Jeroen Boschma <boschma@fel.tno.nl> wrote in message news:<415BDABB.FE640604@fel.tno.nl>...
> ben ito wrote:
> > I will solve Fermat's last theorem.
> > I have formed an infinite number of solutions, using proportional
> > right triangles, that only form integer solutions when n=2 which
> > completes the proof of Fermat's last theorem.
> Your proof sounds something like: because I can form an infinite number
> of solutions for n=2, there just cannot be other solutions. Strange...
Oh, I think it's quite nice. For example, if you have 4 objects in a set,
and you can show that 4 objects in that set are elephants, then it follows
that every member of S is an elephant.
Indeed, for any finite number N, if a set S has N members, and if N members
of S have a certain property, then all members of S have that property.
Now using the fact that infinity is a finite number -- oh, I know this may
be counterintuitive, but that's just because crafty Cantorians *named* things
to make it seem like infinity is infinite -- so, again, using the fact that
infinity is a finite number, we can prove a variety of things.
For example, let S be the set of solutions of X^n + Y^n = Z^n. An infinite
number of them occur for n=1, so all solutions occur for n=1. In particular,
none occur for n>2. Or for n=2, for that matter. And this holds whether
you're working in the ring of integers, or some neo-Harrisian object ring.
On the other hand, because there are an infinite number of solutions to
X^n + Y^n = Z^n, all 4-tuples (X,Y,Z,n) are solutions. Etc.
The thing I like about this method is that it gives Cantor cranks something
to talk about with Fermat cranks. And cranks are usually such solitary
creatures.
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