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

 Messages: [ Previous | Next ]
 Randy Poe Posts: 1,185 Registered: 12/6/04
Re: FLT Discussion: Simplifying
Posted: Jan 18, 2001 8:28 PM

On Fri, 19 Jan 2001 00:22:04 GMT, jstevh@my-deja.com wrote:

>In article <942neb\$dd5\$1@nntp.Stanford.EDU>,
> Michael Hochster <michael@rgmiller.Stanford.EDU> wrote:

>>
>>
>> : (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.)
>>
>> : 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.
>>
>> Yes, that is my position. I would like an explanation of why
>> it is true that if AB = 0, then A = 0 or B = 0. I grant that
>> this statement is true when A and B are integers. However,
>> I would like you to verify it when A and B are funny things
>> like x + sqrt(-1)y and x - sqrt(-1)y (x, y integers).
>>

>
>Hey, I've already seen the post where someone says you guys proved that
>AB = 0, when A = 0, or B = 0 by using x^2 + y^2 = 0.

It's hard to believe you can be so obtuse without trying deliberately.

What the proof uses is that x^2 + y^2 is not zero for all reals x, y
if either x or y is nonzero. Can you see why that is not a good thing
to rely on in a proof that x^2 + y^2 is not zero for all nonzero
integers x, y?

>
>I concede that one could debate the question of whether or not there
>might exist some objects in an infinite ring that could be nonzero and
>multiply times each other to give 0. After all, it's trivally done in
>a finite ring.

You're trainable!

Then perhaps you can be made to understand that mathematical theorems
are built up from a few small starting axioms. A theorem is built on
book, results in Chapter 1 are not proved by using theorems in Chapter
12 that were proved by using theorems in Chapter 1. That would not be
a proof.

Have you ever taken even a single math course? It's not a question of
whether we BELIEVE it's true, it's a question of whether it can be
proved by previously-established results.

- Randy

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