On Tue, 16 Jan 2001 23:16:19 GMT, email@example.com wrote:
>Some, for reasons I'd like them to explain,
The reasons have been given, many times. The primary reason is that if asked to supply a proof, the standard proof relies on knowledge that x^2 + y^2 = 0 for reals. You can't use that in this proof, because you're trying to prove it for the integer case.
> have complained that I >don't know that x + sqrt(-1)y = 0 or x -sqrt(-1)y = 0, if > >(x+sqrt(-1)y)(x-sqrt(-1)= 0. > >(Sort of like if AB = 0, A or B = 0. These people are saying that must >be proven, and that it is a "gap" in my proof that I don't do so.)
It's not "sort of like", it's "exactly like".
> >If so, I'd like them to say that is their position here and we can see >if we can't work that one out.
OK. That's my position here. Let's see if we can't work that one out.
To fill in the gap, you need to prove: AB=0 implies either A=0 or B=0, without relying on the fact that x^2 + y^2 > 0 for all nonzero real x, y.
- Randy >Purists among you may note that I started out in integers as my ring, >and that what I was doing was sticking to my ring.
As soon as you write (x + iy), or (x + sqrt(-1)y), you're no longer "sticking" to your ring, if your ring is the ring of integers with integer addition and multiplication.
What is a ring?
>> >> So, your proof of this simple fact still needs work. >> > >Ok, let's say you're right, and it did need work, and you may think it >still does. I don't have a problem with that. > >What I want to emphasize is that there is a process that can lead to >resolution and it is clear that there are those of you willing to >engage in it based on the fact that you made those comments here. > >So, a reasonable person may now ask, why hasn't that process played out >this way with my claims of a simple proof of Fermat's Last Theorem?
You mean the process where people say "you need to prove this step" and you offer a proof? It hasn't played out because you haven't done the part where you offer a proof of the step in question.