Friday, May 25, 2007

 

JSH: Inconsistency with algebraic integers

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)

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, 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, 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?

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?

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

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.

For instance

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

is an identity as that's what factorizations are, like

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

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

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 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? 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.

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?

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.

Algebraic integers are the center of the number theory universe.

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.

And often with people, proof is not nearly enough, 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!

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.





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