
Re: FLT Discussion: Simplifying
Posted:
Jan 18, 2001 7:42 PM


hale@mailhost.tcs.tulane.edu wrote: > > In article <3a6506aa.270916173@news.newsguy.com>, > randyp@visionplace.com (Randy Poe) wrote: > > On Wed, 17 Jan 2001 01:57:50 GMT, hale@mailhost.tcs.tulane.edu wrote: > > > > >For example, I might be asked to justify the following step > > >(I will assume that I am working in the field of complex numbers, > > >which you have refused to do for some reason): > > > > The reason is that if he admits that saying "x and y are integers" is > > insufficient to discuss the behavior of (x+sqrt(1)y) here, he'd have > > to admit it's insufficient in the FLT proof. > > Yes. > > But, nothing will be lost for James Harris if he would admit that > he is working in the field of complex numbers, and a lot would be > gained since he could use all the theorems proved for complex > numbers. > > However, this would only serve to make his statements to be > meaningful and allow him to define things like "mod" and > "fractional". He would still need to specify a subring of > the complex numbers, since the complex numbers contain "too > many" numbers for what he wants to do. > > James Harris has admitted that he is working in at least two > distinct rings: ring of integers and ring of polynomials. > His statements in the proof also imply that he is working > in the ring of complex numbers and the ring of symbolic > expressions (like sqrt(x^2+y^2)). > > My first impressions were that he was working in just a > subring of the complex numbers. When he claimed that > he was also working in the ring of polynomials, I thought > that would not be possible since he is using the equation > x^5+y^5 = z^5, which is not true in a polynomial ring. > But, he nicely got out of that problem by eliminating > the z and claiming that he is also working in the ring > of symbolic expressions. This clarification has helped > a lot. But, now he is going to the other extreme of
Sorry, but it hasn't helped me. Ring of integers, I understand. Ring of complex numbers, I understand. And if I didn't I could look them up in an algebra book. Ring of polynomials? Well, it's nearly ok. But what indeterminants and what coefficients? But ring of symbolic expressions? Hell, everything that any mathematician has written down is a symbolic expression (and I'm including letters to his Mom). What is a ring of symbolic expressions? What are the elements? What are the operations + and * defined on them?
What James _hopes_ it is, is something in which his "proof" will work; but he can't define it.
> rejecting these known mathematical rings and he is > trying to create his own rings from scratch, which > will demand even more explanations and proofs than > what was originally required. > >  > Bill Hale > > Sent via Deja.com > http://www.deja.com/
 The from address is fictional peter dot percival at cwcom dot net

