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Re: My paper, and the cheaters
Posted:
Sep 18, 2004 7:47 PM
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jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0409171443.51d8ff25@posting.google.com>...
> norabaron@hotmail.com (Nora Baron) wrote in message news:<36024859.0409170732.566a5e55@posting.google.com>...
> > jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0409161404.365eaa1e@posting.google.com>...
> > > I've made some pointed criticisms of math society but if you actually
> > > pay attention you'll realize that the evidence against math society is
> > > nastier than I go into detail about usually.
> > >
> > > Supposedly a correct math result is what's important, but despite my
> > > having a quite correct paper, which was to be published, sci.math'ers
> > > managed to get it yanked IN ONE DAY with some hostile emails.
> > >
> > > The paper has been by a lot of editors and mathematicians and to date,
> > > no major error has been found, which I say because there was one minor
> > > error that actually got pointed out by a sci.math poster.
> > >
> >
> > Please do not ever again claim to be an honest person.
> > Your "proof" contradicts known mathematics. At least 4
> > counterproofs have been given. Dale Hall's counterproof
> > can be checked with simple arithmetic. The exact spot
> > in your "proof" where you make your major error has been pointed
> > out repeatedly. You know all this and yet you continue to
> > deny it.
>
> That's not true.
>
> In fact, I don't disagree with much of what you say.
>
> And I'd like you to admit that in a post, so that I can move on to
> what I actually *DO* say.
>
> First though, I need you to read what I have below and acnowledge that
> you see the agreement on a key point.
>
What??? You want people to agree to your own statement that
you understand and accept a proof? Why don't you just say
you accept it and go on? Why the game-playing?
>
> >
> > Below is one of the simplest counterproofs. Feel free
> > to point out errors (assuming you are still interested in
> > math as opposed to social studies). This is, incidentally,
> > for your future reference, what real proof is supposed to
> > look like.
> >
> > ================================================================
> >
> > James Harris has written a paper called "Advanced Polynomial
> > Factorization" in which he claims the following: if the
> > polynomial
> >
> > 65*x^3 - 12*x + 1
> >
> > is factored in the form
> >
> > (a1*x + 1)*(a2*x + 1)*(a3*x + 1),
> >
> > where a1, a2 and a3 are algebraic integers, then exactly
> > two of a1, a2, and a3 are divisible in the algebraic integers
> > by sqrt(5), and the third one is coprime to 5.
> >
> > It should be noted that -a1, -a2, and -a3 are roots of
> >
> > x^3 + 12*x^2 - 65.
> >
> > That Harris's claim is false can be seen from the following:
> >
> > ==========================================================================
> >
> > Assume m(x) is an irreducible monic polynomial with integer coefficients
> > and algebraic integers a and b are two roots of m(x).
> >
> > Theorem. If p is a nonzero rational integer and a is divisible by
> > sqrt(p) in the algebraic integers, then b is also divisible
> > by sqrt(p).
>
> That last should say, in the algebraic integers.
>
> Theorem accepted. Proof not needed here so I deleted it out to focus
> on what's important. It is in fact true that if 'a' is divisible by
> sqrt(p) in the algebraic integers then b is also divisible by sqrt(p)
> ***in the ring of algebraic integers***.
>
Seems obvious that's what she's saying.
> Concede agreement "Nora Baron" and then I'll explain the rest.
>
She did I believe.
>
> >
> > This polynomial is monic and irreducible with integer coefficients.
> > By the theorem above, if one of the roots is divisible by sqrt(5),
> > then they all are. This is not possible because the product of the
> > roots is 65 = 5 * 13. Therefore Harris's claim that ANY of the
> > roots are divisible by sqrt(5) is false.
>
>
> The poster has shifted from the true claim--that the result applies to
> algebraic integers--to a far vaguer and more inclusive claim,
> basically that it applies in general.
>
I don't think that was her intention. I think she
showed that a/sqrt(5) is not an algebraic integer. Look
at her proof. She isn't claiming more than that.
> Repeatedly, posters keep making claims true in the ring of algebraic
> integers, I accept those claims in that ring, and they then act like I
> don't!!!
>
> I repeat, the result "Nora Baron" gave is correct *in the ring of
> algebraic integers* and I now challenge that poster and others in that
> camp to finally and for once concede that I am not arguing against
> that point.
>
You want the people in "that camp" to agree that you
agree with them ?
> Then I'd like, with the permission of "Nora Baron" to explain exactly
> what my proof actually says.
>
You need PERMISSION to do this ???
> But first I want the poster "Nora Baron" to accept that I am not
> challenging on this specific point.
>
> That's the first step.
>
> It's up to that poster to respond.
>
Like I say, she did.
Incidentally, what did they say about APF at the journal
to which you submitted it earlier in the summer?
Andrzej
>
> James Harris
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