
Re: FLT Discussion: Simplifying
Posted:
Mar 17, 2001 11:59 PM


In hyperintegers, not FLT.
Peter Percival wrote:
> 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

