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

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Charles H. Giffen

Posts: 796
Registered: 12/8/04
Re: FLT Discussion: Simplifying
Posted: Jan 16, 2001 11:04 AM
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jstevh@my-deja.com wrote:
>
[snip]
> Given x^2 + y^2 = 0, x and y nonzero integers, show that no solution
> exists.
>
> Proof by contradiction:
>
> (x+sqrt(-1)y)(x-sqrt(-1)y) = x^2 + y^2 = 0, so
>
> x = sqrt(-1)y *or* x = -sqrt(-1)y.
>
> There doesn't exist an integers that multiplies times itself to give a
> negative number, and an integer can't be the product of an integer and
> a non integer, so there's a contradiction.
>
> First off, it's worth noting that I'm treating the sqrt(-1) as an
> *operation*.


*Operation*??? -- do you mean something like a lobotomy?

How can you multiply an *operantion* by an integer? -- there you go
again making up inane terminology (*operation*) with no definition
or discussion of its properties -- using it in ways that are not
defined for your new (and useless!) terminology. You must be the
consummate bovine fecal artist on this planet.

Certainly, you do not understand what is wrong with your proof,
even though it contains some (*possibly*) correct formulae, but no
explanation or reasoning to put them in context and to justify
them.

If you cannot get this proof straight or understand just what part
of mathematics is necessary to prove this simple claim, just think
how much worse your attempts to prove FLT look to the rest of the
world.

Evidently, you do not understand that, in order to prove that the
complex numbers are a field (or integral domain), you need *first*
to know that, for any real numbers x, y not both zero,
x^2 + y^2 != 0 -- and thus you *cannot* use the complex numbers
to prove x^2 + y^2 != 0 if at least one of the real numbers
x, y is nonzero.

As I pointed out a long time ago -- but you seem to block all my
e-mails and postings -- the proof that x^2 + y^2 > 0 (and hence
!= 0) relies on the *order* properties of the reals -- namely,
that the square of any nonzero real is positive and the sum of
two nonnegative reals is positive if at least one of them is
positive.

I think some of you live under the false notion that
> something like sqrt(2) is the actual number. Nope. It's an operation
> that tells you something about that number, like that it multiplies
> times itself to give 2. We also use it handily as a shorthand
> representation for the actual number, which is also sometimes
> represented by 1.414...
>


sqrt( ) is an "operation" -- i.e. a function -- at least to most
people. It associates to x one (or more than one, depending upon
the context) square root of x, i.e. an element t such that
t^2 = x.

> No human being has ever seen or ever will see the actual number that we
> can conveniently represent by sqrt(2).
>


I see sqrt(2) almost every time I look at an isoceles right
triangle -- don't you?

> We're just limited that way.
>


You may be limited that way -- others are not.

> So, I use sqrt(-1) in a proof that's dealing with integers, and I don't
> care that there's such a thing as i = sqrt(-1). All I care about is
> that I've found this thing that isn't an integer.
>


If you are using it in a proof that deals with integers, then, at the
very least, it [ sqrt(-1) ] had doggone well better lie in a ring
that contains the integers, such as the complex numbers or the Gaussian
integers -- *not* in the integers modulo 5 (or 6) -- "integers modulo
m" (m > 0) do *not* contain the integers!

> Ok, jumping to my proof of FLT for p=5. I prove (and no one disputes
> this) that
>


Jumping from one false argument to another...

> [(v^5 + 1) z^2 -(5v^3 + sqrt(5v^6 - 20v))xy/2] [(v^5 + 1) z^2 -(5v^3 -
> sqrt(5v^6 - 20v))xy/2] = 0(mod (x+y+vz)/h), when x^5 + y^5 = z^5, and
> for the simplest case h = (x+y)^{1/5}.
>

[snip]

--Chuck Giffen






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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