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 >call it. > >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.