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

 Messages: [ Previous | Next ]
 Dik T. Winter Posts: 7,899 Registered: 12/6/04
Re: FLT Discussion: Simplifying
Posted: Jan 19, 2001 6:24 AM

In article <947ucs\$4d2\$1@nnrp1.deja.com> jstevh@my-deja.com writes:
> In article <G7A90y.7r4@cwi.nl>,
> "Dik T. Winter" <Dik.Winter@cwi.nl> wrote:

...
> > You assume that whenever AB = 0 for your funny
> > things that either A = 0 or B = 0 or both. But you have to give a proof
> > of that because there are many funny things in mathematics where that
> > does *not* hold. And it has been *proven* for the complex numbers, but
> > that proof actually uses that x^2 + y^2 can not be 0 unless both x and
> > y are 0. Just the thing you want to prove. So because you rely on that
> > fact for the complex numbers you are reasoning in a circular fashion. It
> > is like (with either x or y nonzero or both):
> > x^2 + y^2 != 0 because whenever AB = 0 either A = 0 or B = 0 and the
> > latter is true because x^2 + y^2 != 0.
> >

>
> Then I notice that (x+sqrt(-1)y)(x-sqrt(-1)y) = 0 because x^2 + y^2 = 0.
>
> And remember, at this point as far as I'm concerned x and y are still
> integers!

Up to this point I had no complaint at all, so why pull it out of the box
again?

> Why?
>
> Because if I know they aren't at this point then I already must have
> reached the point of contradiction. And then, your argument must be
> that the proof I've given is too long!!!

Up to this point I see *no* contradiction at all.

> What some of you appear to be arguing is that when I realize that this
> thing, sqrt(-1) is not an integer, I must stop, and pull out a book on
> complex number theory.

Nope. You conclude that either (x + sqrt(-1)y) = 0 or (x - sqrt(-1)y) = 0,
without giving proof of that. In another article you said you declined
to give a proof of this. Interesting, because a proof is *essential*.
You can not pull such statements out of your hat and claim they are true.

> I'm looking for something that pushes me outside of integers because
> that's what I want to prove must happen!

Tsk. Your initial use of sqrt(-1) pushes you out of the integers already.

> You say the textbooks do it a different way, and I assume that assaults
> your sense of order for me to show it this way because if everybody has
> done it one way, you seem to assume that any other way is wrong.
>
> Then prove it's wrong!!!

Textbooks prove that in this case AB = 0 implies either A = 0 or B = 0 or
both. Something you are not willing to do for some reason. I presume
you are not able to do it?
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

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