Re: JSH: A simple error

On May 27, 8:45 am, jst...@xxxxxxxxx wrote:
Posters in attacking my proofs showing inconsistency with the ring of
algebraic integers routinely move outside the ring. Here is a post
meant to show you how they do it.

In the ring of integers, consider x^2 + 3x + 2 = 0, which of course
factors as

x^2 + 3x + 2 = (x+2)(x+1)

and now solve for it using the quadratic formula, but kind of weird by
NOT resolving the square root then

x = (-3 +/- sqrt(1))/2

and now make the substitution, x=2y, so you get

4y^2 + 6y + 2 = 0, so you can divide by 2 to get

2y^2 + 3y + 1 = 0,

and your solution now becomes

y = (-3+/- sqrt(1))/4

which is two solutions where one is not an integer.

So you moved outside the ring of integers.

So what's the trick?

Well, with integer solutions you can resolve the square root and throw
away one solution, which is what most people routinely do, so they say
that sqrt(4) = 2.

When you do not resolve the square root--or cannot when it is non-
rational--then you cannot throw away the other solution, so it gets
dragged along, and if you do what posters typically do in replies
against my research, and blanket divide a variable like x above so
that you divide MORE THAN ONE SOLUTION you end up pushed out of the
ring of algebraic integers.

When I've pressed them on the reality that the sqrt() returns more
than one value, posters have replied with derision noting that
mathematicians have DEFINED it to have one value, so that they can
continue their trick unabated, as if it were a legitimate criticism
against my research.

But as I've noted repeatedly, the ring of algebraic integers is
inconsistent, and you cannot prove that is is from within the ring!

It is too weak as a ring, to allow you to prove that certain results
are not within it, so posters are forced to go outside the ring to
try and make their objections.

As a reminder, the updated paper--I had to clear out some errors noted
by Rick Decker--is linked to at my Extreme Mathematics group:

http://groups.google.com/group/extrememathematics/web/non-polynomial-...


Seems only fair if we are going keep arguing with you to meet you
halfway. So I'm looking at the paper above, and at the end of
Section 3 I come to this:

(49x^2 - 7Q(x))5^2 + (-1 - 3x - 5Q(x))(5)(7) + 7^2

= 0 (mod(r + 7 + 5(1 + 7x)))

which I think is supposed to be an identity. Right? It should be
true regardless of the values of r and x and Q(x). Right?

But then I see that inside the mod expression on the right
there is an "r", and there is no "r" on the left. Peculiar. So
maybe I should true substituting in some values for x and r and
see what happens. So say x = 1 and r = 1 and Q(x) = -2.

The left side is then

(49 + 14)*25 + (-1 - 3 + 10)*35 + 49 = 1834.

The "mod" expression is

1 + 7 + 5*8 = 48.

So, is 1834 = 0 (mod(48)) ? No. 1834 = 10 (mod(48)).

Maybe you should check my arithmetic, see if I made a
mistake.

I let Q(x) = -2x. Of course Q(x)*7*5^2 is added and
subtracted on the left side, so it shouldn't matter at all
what Q(x) is. That's not the mistake.

So I went back in your derivation a little bit. At one
point you have

r^2 + 2rs + s^2 = v^2 t^2 (mod r + s + vt),

which is fine. But then you say:

"and I can now subtract

r^2 + rs - (2 + 2xt + tQ(x))st + s^2 = (1 + 2xs + sQ(x))t^2"

But right here, the left side of this equation in general
is not equal to the right side - you can see that with some
simple substitutions also - and it's not given as a modular
equation. I mean, look, there is no "r" on the right side
of the equation. The two sides cannot be equal in general.
So this might be the cause of the problem with the later
equation.


It may be that you are saying, "I am going to assume the
following equality,

r^2 + rs - (2 + 2xt + tQ(x))st + s^2 = (1 + 2xs + sQ(x))t^2

and subtract it from both sides of my modular tautology, and
the equality just above is what I call my conditional."

But how do you justify that conditional? It certainly is
not true in general.

I mean, this part of the argument looks like the following:

I start with a modular tautology in terms of variables r, s,
v, and t.

I make up an equation involving the variables r, s, v, t,
and x.

I subtract each side of the made-up equation from each side
of the modular equality.

I end up with the equation I want.

But I still don't see how you justify the made-up equation.
It looks like it just came out of thin air. Please explain.

-------------------------------------------------------------

But there is I think even a bigger problem. You talk about
tautological spaces and it's clear that you are trying
to derive the equation

(49x^2 + 7Q(x))5^2 - (3x + 1 + 5Q(x))(5)(7) + 7^2 = 0

from modular tautologies. But that in itself looks like a
problem to me. A modular equation is not an equation.
Something like


(49x^2 - 7Q(x))5^2 + (-1 - 3x - 5Q(x))(5)(7) + 7^2

= 0 (mod(r + 7 + 5(1 + 7x)))

does not imply that

(49x^2 - 7Q(x))5^2 + (-1 - 3x - 5Q(x))(5)(7) + 7^2 = 0.

You can't just remove the "mod" arbitrarily. But that
is what you seem to be doing. Can you explain this?

I mean, 6 = 0 (mod 2) is true, but 6 = 0 is not true.
You can't just throw away the "mod". You start with
the tautology

r + s + vt = 0 (mod(r + s + vt))

but it's not a tautology at all if you leave out the
"mod" part - that is, you cannot conclude, for example,
from your tautology that

r + s + vt = 0.

What's your explanation on this?


One crucial addition to the paper besides error fixing is the noting
that I use identities mostly, and one equation that is not an
identity,

Yes - but how do you justify that equation??? Do you just declare
it to be true by fiat?


so that equation MUST drive the conditions, and it can be
placed easily enough in the ring of algebraic integers.

This result is one of the biggest in mathematical history
demonstrating an actual inconsistency with a well-known mathematical
object, which mathematicians have unknowingly used for over a hundred
years without understanding how it can lead to false arguments that
appear to be proofs when they are not.

Readers should note that I have multiple mathematical discoveries at
this time where all have been vigorously attacked by posters who
clearly have a need to deny any mathematical result if they feel it
will give credence to my research.


Sorry, I think the only discovery you can claim is your
algorithm for counting primes.



They are dogmatic in their resistance, which is part of the reason I
call these continuing arguments against mathematical proof--


You know, if your argument depends on an equation that you just
plucked out of thin air, I don't see how it can be regarded as
a proof.


and even
publication in a peer reviewed mathematical journal--the Math Wars.

I have rebutted the sci.math newsgroup which killed a mathematical
journal with false claims, and bears a responsibility to accept
accountability.


All kinds of assumptions are being made here. For example, the
assumption that your article was peer-reviewed. If that is true,
why did the editor send you a copy of an e-mail from W. Dale Hall,
sent to him AFTER the article was published, claiming it was one
of the peer reviews? And if it WAS one of the peer reviews, why
would they have published the paper, since it said your "proof"
was wrong? And how did the temporary publication of your paper
lead to the death of the journal? I mean, if your paper had
anything to do with it at all, it must have been that the journal
was discredited because of that publication - people must have
thought that that publication was a fatal mistake.

There is also the fact that you knew, before that paper was
published, that it contained errors. You admitted that prior
to publication. The "published" version still contains the
errors that you conceded months before the paper was in the
journal. You knew this, but you didn't withdraw the paper.

This was a shameful episode. Shameful for the journal
and its editor, because he was completely slipshod. He told
you an outright lie. He yanked your paper with no explanation.
He treated you like you were an insignificant nobody. Don't
try to blame posters here for that; the editor is to blame.
But also, you lied. You knew your paper was wrong but you
didn't withdraw it. Arguably you were committing fraud.

Why do you keep bringing this up? It just makes you look
bad - both mathematically incompetent and deeply dishonest.

Marcus


James Harris


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