Date: Dec 29, 2012 3:47 AM
Subject: Re: request for help with lemma (algebra, summations)
Orange Pekoe wrote:
>Let me start by saying that the link isn?t really a lemma, but
>since it?s probably not a proof either, I didn?t know what to
>I should also quickly add that I?m not a mathematician - or even
>close ? so I don?t really expect to be taken seriously. Even so,
>I hope you will take a look at the link and try to get at least
>a few lines into the equations. The whole thing is well under 2
>pages printed so this is at least guaranteed not to waste (much)
>of your time.
>I never use the proper name of the problem but that will be
>immediately obvious so you might want to refrain from sipping
>any beverages until you get past the first couple of paragraphs
> ? for the sake of your keyboard and monitor.
>I know I'm making light of this, but I am serious about wanting
>to know if I might be on to something.
Your attempt is likely worth nothing as far as the mathematics
go, however a possible value is that it may spur you on to a
more serious self-study of math in order that you may eventually
be able to recognize and construct valid proofs.
Your assumption a < b < c is innocent, but your assumption
x < y < z requires justification. It's not immediately clear
that you can get away with that.
Very suspect is your later "simplification" where you assume
a^2 + b^2 = c^2. That's effectively assuming n = 2, but the
whole point is to start with the assumption that n > 2.
Perhaps the most blatant flaw is that, as far as I can see,
you never use the assumption that a,b,c are positive integers.
I don't see any mention of divisibility or congruences or
any reasoning that would fail if a,b,c were only assumed to
be positive reals. I mean, the equation a^3 + b^3 = c^3
_does_ have solutions for a,b,c positive reals -- simply
choose a,b > 0 and let c be (a^3 + b^3)^(1/3).
Besides that, your lack of knowledge of how to express things
rigorously renders your proof mostly unreadable, so for now,
aside from the objections I made above, I won't try to decipher
it any further.