Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: FLT Discussion: Simplifying
Replies: 65   Last Post: Mar 17, 2001 11:59 PM

 Messages: [ Previous | Next ]
 hale@mailhost.tcs.tulane.edu Posts: 229 Registered: 12/8/04
Re: FLT Discussion: Simplifying
Posted: Jan 17, 2001 12:30 AM

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
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/

Date Subject Author
1/15/01 jstevh@my-deja.com
1/15/01 Dik T. Winter
1/16/01 Charles H. Giffen
1/16/01 jstevh@my-deja.com
1/16/01 Randy Poe
1/18/01 jstevh@my-deja.com
1/18/01 Michael Hochster
1/18/01 Peter Johnston
1/18/01 Randy Poe
1/18/01 Doug Norris
1/16/01 Doug Norris
1/16/01 Randy Poe
1/16/01 Dik T. Winter
1/18/01 jstevh@my-deja.com
1/19/01 Dik T. Winter
1/19/01 Randy Poe
1/20/01 jstevh@my-deja.com
1/20/01 oooF
1/21/01 hale@mailhost.tcs.tulane.edu
1/21/01 Peter Percival
1/21/01 Randy Poe
1/26/01 Franz Fritsche
1/19/01 gus gassmann
1/20/01 jstevh@my-deja.com
1/20/01 Doug Norris
1/26/01 Franz Fritsche
1/16/01 hale@mailhost.tcs.tulane.edu
1/16/01 Randy Poe
1/17/01 hale@mailhost.tcs.tulane.edu
1/18/01 jstevh@my-deja.com
1/19/01 hale@mailhost.tcs.tulane.edu
1/20/01 jstevh@my-deja.com
1/21/01 hale@mailhost.tcs.tulane.edu
1/18/01 Peter Percival
1/19/01 hale@mailhost.tcs.tulane.edu
3/17/01 Ross A. Finlayson
1/16/01 hale@mailhost.tcs.tulane.edu
1/18/01 jstevh@my-deja.com
1/19/01 hale@mailhost.tcs.tulane.edu
1/29/01 jstevh@my-deja.com
1/19/01 Dik T. Winter
1/21/01 Dennis Eriksson
1/15/01 Michael Hochster
1/16/01 jstevh@my-deja.com
1/16/01 Michael Hochster
1/18/01 jstevh@my-deja.com
1/18/01 Peter Percival
1/18/01 Randy Poe
1/19/01 oooF
1/21/01 Dik T. Winter
1/21/01 oooF
1/18/01 Edward Carter
1/19/01 W. Dale Hall
1/19/01 Michael Hochster
1/16/01 Randy Poe
1/16/01 Randy Poe
1/17/01 W. Dale Hall
1/17/01 W. Dale Hall
1/19/01 oooF
1/16/01 Charles H. Giffen
1/16/01 David Bernier
1/16/01 jstevh@my-deja.com
1/18/01 Arthur
1/30/01 plofap@my-deja.com
1/30/01 plofap@my-deja.com
1/30/01 plofap@my-deja.com