Re: JSH: Inconsistency with algebraic integers

On May 25, 4:25 pm, jst...@xxxxxxxxx wrote:
Now at least it is possible to carefully explain exactly what is wrong
with the ring of algebraic integers as using it you can appear to
prove two different and opposite things.

So I can start with an identity, the factorization:

175x^2 - 15 x + 2 = (f(x)+2)(g(x)+1)

That's not an identity, because at this stage - the starting
stage - you have not defined f(x) or g(x). An identity is
something like

x^2 - 1 = (x + 1)*(x - 1),

which is true regardless of what number x is. But

175x^2 - 15 x + 2 = (f(x)+2)(g(x)+1)

is not true for all possible definitions of f(x) and g(x); it
is not an identity.


which I do in my paper, and proceed to use only identities and a key
monic expression in my derivation, to appear to prove that one and
only one root of

y^2 - 6y + 35 = 0

has 7 as a factor, in the ring of algebraic integers.

That is not in doubt and has not been refuted,


It is false and refutations have been provided for you up
the ying-yang.


and in fact it stands
as the beginning of the objections raised against my research, as you
can then go, say, to the field of algebraic numbers and prove that 7
is NOT a factor of EITHER root in the ring of algebraic integers!!!

That is the basis of my rebuttal to posters who have long argued
against my research, even attacking it in emails to the math journal
that published a key paper of mine, and died after the editors trusted
them.

I have rebutted these posters but they persist in ignoring basic
proof, like that all their own claims of counterexamples depend on
going outside the ring of algebraic integers,

If you are going to prove that a number, say 'e', is not an
algebraic integer, it stands to reason that at some point in
the proof, though possibly not until the very end, you are
going to have to say that e is outside the ring of algebraic
integers! You are trying to impose an impossible criterion: that
in order to prove that e is not an algebraic integer, you are
allowed to consider only expressions that stay within the ring
of algebraic integers.


and that my work clearly
shows using identities and expressions valid within the ring of
algebraic integers, you can appear to prove that 7 is a factor of only
one root.

So why is this a big deal?


It's not a deal at all, let alone a big deal. What you "appear to
prove" is just plain wrong.


Because mathematics is very particular about error. If people deny
the error then they can "prove" things that are mathematically NOT
true, and if you built a career on faux proofs, would you want that
known?


Good question. You should think hard about that.


My key paper proving the inconsistency problem starts with an
identity.

Are you now claiming mathematics is inconsistent?


I use identities throughout much of the paper, only at one
point finally introducing a single conditional expression:

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


Conditional on what?


If you know anything about mathematics at all then you should know
that identities do not do anything in terms of adding properties, or
setting conditions.

The paper uses only identities up to a crucial point when one
conditional is introduced.


This is wrong. You want to conclude something about g(x).
You note that

7g(x) = 5a_2(x).

Which implies that

g(x) = 5a_2(x)/7.

That is, if you want to make a statement about g(x), you have
to permit division (by 7 in this case) as a valid operation. But
it is not a valid operation in general in the ring of algebraic
integers.


For instance

175x^2 - 15 x + 2 = (f(x)+2)(g(x)+1)

is an identity


It is NOT an identity until you provide a definition of
f(x) and g(x). There is a difference between an equation
(true only for certain solutions) and an identity (true
regardless of the values of variables).


as that's what factorizations are,

They are not. I can write

A*B = 484

That is formally a factorization. It is not an identity. It
is just an equation which is true for certain values of the
factors A and B.


like

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

is an identity, and identities are just true, not conditionally true.


But

175x^2 - 15 x + 2 = (f(x)+2)(g(x)+1)

is true conditional on what f(x) and g(x) are. It is not true for
most definitions of f(x) and g(x). And at this point you have not
defined them.


If you read over my paper you can step through an argument using
operations valid in the ring of algebraic integers, like I multiply
both sides by 7, and re-order a bit to get

7(7(5^2)x^2 - (3)(5)x + 2) = (f(x) + 2)*(7g(x) + 7)

and I do that so that I can make a substitution using

5a_2(x) = 7g(x)

and I replied recently to a poster claiming that my argument fails
because I try to use division, as he wrote:

g(x) = 5a_2(x)/7


The object of your argument is to make a statement about g(x).
There is no escaping the fact that

g(x) = 5a_2(x)/7.

If you take this to be the DEFINITION of g(x), note that it
depends on division.

The paper uses identities and expressions valid in the ring of
algebraic integers to appear to prove a result that is not true in
that ring if and only if with integer x, f(x) and g(x) are not
rational.

If they are rational, then hey! It turns out that everything flows
just fine and you're in the ring of algebraic integers. If they're
not rational then hey! The freaking argument still says you're in the
ring of algebraic integers, if you start assuming that

175x^2 - 15 x + 2 = (f(x)+2)(g(x)+1)

is true in that ring, but you can go to a field and prove that you're
not in the ring.

But wait, factorizations are identities, right?

Wrong. AB = 160 is formally a factorization. It is not an
identity.


So how can you be out
of the ring with the factorization? Oh wait, it must be about the
conditions on f(x) and g(x) as to how they're derived right? As
identities do not give properties.


You are not starting with an identity. At the outset, f(x)
and g(x) are undefined. Your initial equation is not an
identity because it is not true for all possible values of the
variables. If you start with an identity and then derive
f(x) and g(x) from that, you will find that the definition of
g(x) involves division by 7. Division is not a ring operation.


BUT, the conditional is given in my paper, and with it monic and
clearly in the ring of algebraic integers with integer x, you are
still forced out of the ring!

Hard to understand? Finding yourself confused?


I don't, not at all. You do. You have completely lost clarity in
your thinking on this. You have thoroughly confused yourself.


That is what faux mathematics does. It is quirky, problematic and
hard to grasp logically if you believe it is correct.

Mathematics abhors inconsistency.

Now I've proven my case multiple ways over a period of years and even
got published, but I feel like early scientists must have felt
fighting religious leaders angry at the earth supposedly not being the
center of the universe.


You've got it backwards. You are more like a religious
leader trying to convince early scientists that they should not trust
what they can see, touch, taste, smell, or hear for themselves - they
should trust only you and the voices of the gods that only you can
hear.


Algebraic integers are the center of the number theory universe.


They're a somewhat specialized field of study. There is a lot of
very good and important number theory that does not depend on the
algebraic
integers.


People who grew up on these mathematical ideas that are flawed, who
built careers on these mathematical ideas that are flawed do NOT WANT
TO ACKNOWLEDGE that their knowledge is flawed.

Any more than deeply religious people wished to accept that the earth
was not at the center.

You see, they were very invested as well.

These battles keep playing out in human history, where it is about one
group of people who get a vested interest in being wrong, and usually
one man who is fighting for the truth, with only proof on his side.


If one man thinks he is right and everyone else thinks he is wrong,
there is an overwhelming chance that he is wrong. A few famous
counterexamples go the other way. Saying "usually" as you do above
is completely unjustified.


And often with people, proof is not nearly enough,

1. You don't have proof.

2. You are not qualified to say you have proof. You have been
wrong about having proof far, far, far too often to make that
claim.

3. Saying you have a proof does not make it a proof. That is
true for everyone. You are no exception.


so the wasted years
go by, with people fighting with a will to be wrong, so that they can
hold back knowledge for just one more year if they can, or longer, as
they can only see themselves and how they feel.

They only care about their own needs and cannot be bothered to care
about the fate of the entire species as if they could be that great,
then they wouldn't be fighting the truth in the first place!


Oh good grief. Get over it already! Even if you were right, you
would be blowing this grossly out of proportion. None of us are
that important. The fate of our species is not at risk, not because
of this stupid little tiff. More likely you should worry about some
accelerator creating a Higgs boson and turning the earth into a
black hole.


That mathematicians around the world can continue with a demonstrated
inconsistency making their efforts wasted is all about how small they
are, and not at all about brilliance.

If there were any truly great mathematicians out there, they would
fight to end the use of the faux math, not sit and hope no one
notices, and the human race be damned.


Is it really that inconceivable to you that you are just ...
plain ...
wrong ??? I mean, given your track record, given the dozens of
flaming howlers you have fought tooth and nail to defend, given
your asinine posturing and whining and apolcalyptic predictions and
threats to
have the Army or the courts - Alberto Gonzales, perhaps - round us
all
up and strip us of our positions and burn our textbooks and tar and
feather us and have angry mobs jab us with pitchforks - given your
recent
huffing and puffing about hauling us all into court - given all this,
and the many, many times you have had to meekly creep off with
perhaps
a single 'Oops', given the fact that you have NEVER ONCE, for
example, proven Arturo Magidin wrong (yet are now trying to strip
him of his right to teach - get his alma mater to rescind his
PhD) - given all this despicable incredibly stupid loser behavior,
where in the bloody hell, man, is your humility???

Marcus.

James Harris


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