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

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Peter Johnston

Posts: 19
Registered: 12/12/04
Re: FLT Discussion: Simplifying
Posted: Jan 18, 2001 8:05 PM
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Isn't the outcome worth it? If you can convince us that the proof is valid,
WHY not?

Peter


<jstevh@my-deja.com> wrote in message news://947tfo$3lu$1@nnrp1.deja.com...
> In article <3a64de9b.260659399@news.newsguy.com>,
> randyp@visionplace.com (Randy Poe) wrote:

> > On Tue, 16 Jan 2001 23:04:15 GMT, jstevh@my-deja.com wrote:
> >

> > >> > (x+sqrt(-1)y)(x-sqrt(-1)y) = x^2 + y^2 = 0, so
> > >> >
> > >> > x = sqrt(-1)y *or* x = -sqrt(-1)y.

> > >>
> > >> James, you have to *prove* that last step. You cannot rely on the

> > >standard
> > >> proof because it uses: x^2 + y^2 <> 0 whenever x != 0 or y != 0.
> > >
> > >I think some people may be surprised that you are essentially calling
> > >this a gap.

> >
> > Quick poll: Anyone who is surprised that this is being called a "gap"
> > (remove the word "essentially"), chime in.
> >

> > >
> > >My comment to them is that it's the same thing being done with the
> > >proof of Fermat's Last Theorem.

> >
> > Yes. This proof was introduced into this forum because the logical
> > fault is similar.
> >

>
> Ok folks, here you are hearing that strange statement again.
>
> I want to emphasize that this guy is arguing that what I have above is
> not a proof.
>

> > >
> > >As for your other statement, it doesn't make any sense to me.
> > >
> > >What's going on is simple though. I have that x^2 + y^2 = 0, and I
> > >know that x^2 + y^2 = (x+sqrt(-1)y)(x-sqrt(-1)y),

> >
> > You don't know this unless you define the context in which you are
> > operating.
> >

>
> See folks? I just don't get why I have to repeat over, and over, and
> over again that x and y are integers.
>
> Do you?
>
> Given that x and y are integers, how many of you out there have any
> doubt that x^2 + y^2 = (x+sqrt(-1)y)(x-sqrt(-1)y)?
>
> Well, this guy certainly seems to doubt it, and not only that he's
> doubts it so much that he decided he'd post that doubt with emphasis.
>
> What gives?
>
> Remember, he's taking this position as part of saying that my proof of
> Fermat's Last Theorem is wrong.
>
> That's the big picture, and you should keep it in mind.
>

> > > so
> > >
> > > (x+sqrt(-1)y)(x-sqrt(-1)y) = 0,

> >
> > > so
> > >
> > > x+sqrt(-1)y = 0 or x-sqrt(-1)y=0,

> >
> > And you don't know this automatically.

> > >
> > >and that goes to the question of how long a proof has to be.

> >
> > No, it goes to the question of whether a statement preceded by the
> > word "so" actually follows logically from the statement that precedes
> > it.
> >

> > >
> > >As you can see, some people will force you to outline simple steps

> that
> > >others would find unnecessary.
> >
> > And the person providing the proof should be able to outline those
> > steps, even if he/she finds it unnecessary.
> >
> > So humor us. Even though it's unnecessary, prove that
> >
> > ab = 0, for complex a, b (they're COMPLEX, not integers, OK?)
> >
> > implies
> >
> > a = 0 or b = 0.
> >
> > It's not an axiom, it's a theorem. So it's provable. Just for grins,
> > offer up a proof. Even though it's unnecessary. Waste a few electrons
> > on us. It can't hurt.

>
>
> It doesn't matter whether or not a and b are complex or not.
>
> The only possible issue might be made by using something like 3(2)=0
> (mod 6), but we're not talking about a finite ring.
>
> As for me proving that if ab = 0, a or b equals 0, I'm not interested
> in doing that.
>
> If you need that proof to understand what I'm talking about, oh well.
>
> I'll just worry about the people who don't have a problem with that.
>

> > >
> > >That bit of arbitrariness is used by some people to claim that a

> proof
> > >isn't.
> >
> > So isn't the obvious answer to add a few lines to prove the assertion?
> > If you did, everyone would shut up. Saying "I don't have to" doesn't
> > do anything to answer the objections. What's the harm in explaining
> > what mathematical principle justifies the conclusion?
> >

>
> I did that. You folks just keep asking for more and more detail, like
> you asking for me to prove that if ab = 0, a or b = 0.
>

> > >
> > >>
> > >> > First off, it's worth noting that I'm treating the sqrt(-1) as
> an
> > >> > *operation*. I think some of you live under the false notion
> that
> > >> > something like sqrt(2) is the actual number.
> > >>
> > >> I must be dense, but what the heck do you mean? If it is not a

> number
> > >> you have to define how to do multiplication of operations with
> > >numbers.
> > >>
> > >
> > >The sqrt(2) is a representation of the number that multiplies times
> > >itself to give 2 (notice how circular that is).

> >
> > That makes it a number, not an operation. It stands for the NUMBER.
> > That is not at all circular.

>
> Isn't it? Like I've said, we don't put down 1+1 to represent 2.
> The '+' is an operator. The sqr() is an operator. We use the
> operation to represent the square root of 2, or we write 1.414..., or
> something similar.
>
> Why you would argue such a simple point is beyond me.
>

> >
> > >I think I should mention that there's also a question of trueness.
> >
> > Don't know what you mean by this, except that perhaps you are looking
> > for a vote on the truth value of an assertion.
> >
> > In mathematics, normally a sequence of logical deductions serves to
> > demonstrate truth. Got that?
> >
> > SEQUENCE of LOGICAL deductions.
> >

>
> You don't have to be condescending *and* obnoxious.
>
> I think most folks out there can conceive of a statement as being
> either true or false. 1=2 is a statement that is false. 2 = 2 is true.
>
> Again, why you would argue over something this simple is beyond me.
>
> And I think it pertinent that you deleted out the statement that was
> being referred to.
>
>

> > For instance, please offer a sequence of logical steps showing that
> > for two complex numbers a and b, ab=0 implies a=0 or b=0.
> >

>
> And now we have that again...
>

> > Even a one-liner would be better than saying "it's obvious" over and
> > over. Here, I'll start you out: "We can conclude that either a=0 or
> > b=0 because... "
> >

>
> If you want to argue about whether or not ab = 0 means that a = 0, or b
> = 0, then go ahead, but you'll be doing it without me.
>
>
> Sent via Deja.com
> http://www.deja.com/








Date Subject Author
1/15/01
Read FLT Discussion: Simplifying
jstevh@my-deja.com
1/15/01
Read Re: FLT Discussion: Simplifying
Dik T. Winter
1/16/01
Read Re: FLT Discussion: Simplifying
Charles H. Giffen
1/16/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/16/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/18/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/18/01
Read Re: FLT Discussion: Simplifying
Michael Hochster
1/18/01
Read Re: FLT Discussion: Simplifying
Peter Johnston
1/18/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/18/01
Read Re: FLT Discussion: Simplifying
Doug Norris
1/16/01
Read Re: FLT Discussion: Simplifying
Doug Norris
1/16/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/16/01
Read Re: FLT Discussion: Simplifying
Dik T. Winter
1/18/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/19/01
Read Re: FLT Discussion: Simplifying
Dik T. Winter
1/19/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/20/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/20/01
Read Re: FLT Discussion: Simplifying
oooF
1/21/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
1/21/01
Read Re: FLT Discussion: Simplifying
Peter Percival
1/21/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/26/01
Read Re: FLT Discussion: Algebra...
Franz Fritsche
1/19/01
Read Re: FLT Discussion: Simplifying
gus gassmann
1/20/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/20/01
Read Re: FLT Discussion: Simplifying
Doug Norris
1/26/01
Read Re: FLT Discussion: Matrix or not, that's NOT the question...
Franz Fritsche
1/16/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
1/16/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/17/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
1/18/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/19/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
1/20/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/21/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
1/18/01
Read Re: FLT Discussion: Simplifying
Peter Percival
1/19/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
3/17/01
Read Re: FLT Discussion: Simplifying
Ross A. Finlayson
1/16/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
1/18/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/19/01
Read Re: FLT Discussion: Simplifying
hale@mailhost.tcs.tulane.edu
1/29/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/19/01
Read Re: FLT Discussion: Simplifying
Dik T. Winter
1/21/01
Read Re: FLT Discussion: Simplifying
Dennis Eriksson
1/15/01
Read Re: FLT Discussion: Simplifying
Michael Hochster
1/16/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/16/01
Read Re: FLT Discussion: Simplifying
Michael Hochster
1/18/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/18/01
Read Re: FLT Discussion: Simplifying
Peter Percival
1/18/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/19/01
Read Re: FLT Discussion: Simplifying
oooF
1/21/01
Read Re: FLT Discussion: Simplifying
Dik T. Winter
1/21/01
Read Re: FLT Discussion: Simplifying
oooF
1/18/01
Read Re: FLT Discussion: Simplifying
Edward Carter
1/19/01
Read Re: FLT Discussion: Simplifying
W. Dale Hall
1/19/01
Read Re: FLT Discussion: Simplifying
Michael Hochster
1/16/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/16/01
Read Re: FLT Discussion: Simplifying
Randy Poe
1/17/01
Read Re: FLT Discussion: Simplifying
W. Dale Hall
1/17/01
Read Re: FLT Discussion: Simplifying (Grammar fix)
W. Dale Hall
1/19/01
Read Re: FLT Discussion: Simplifying
oooF
1/16/01
Read Re: FLT Discussion: Simplifying
Charles H. Giffen
1/16/01
Read Re: FLT Discussion: Simplifying
David Bernier
1/16/01
Read Re: FLT Discussion: Simplifying
jstevh@my-deja.com
1/18/01
Read Hi - little fun about FLT
Arthur
1/30/01
Read Re: FLT Discussion: Simplifying
plofap@my-deja.com
1/30/01
Read Re: FLT Discussion: Simplifying
plofap@my-deja.com
1/30/01
Read Re: FLT Discussion: Simplifying
plofap@my-deja.com

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