Harristotelian Logic

I think I keep stumbling a bit in trying to explain this thing, so I'm going to keep replying in the other threads, but try to bottomline it in this one so that it makes sense.

Bottomline is that you can try to stay in the ring of algebraic integers with a polynomial you can't factor into polynomials, like

P(x) = 175x^2 - 15x + 2

with a factorization that CAN be done in the ring of algebraic integers:

P(x) = (f(x) + 1)*(g(x) + 2)

where you have f(x) and g(x) that will give you algebraic integers, if x is an algebraic integer.

There are an infinity of such functions.

There are an infinity of them with the requirement that f(0) = g(0) = 0.

Despite that infinity though, a few more steps and no functions out of that infinity can still remain.

And that's as simple as going to

7*P(x) = (a_1(x) + 7)(a_2(x) + 7)

and it's almost simple enough that most of what I did in my previous threads was unnecessary.

Now the a's can't be algebraic integer if f(x) and g(x) are algebraic integer functions.

Or if the a's are algebraic integers, then f(x) and g(x) can't be.

It's that simple.

One way to see what can happen that algebraic integers can't handle is to consider

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

and you may say, trivial. Yeah, well, the ideas here aren't that terribly complicated people as notice you have one root that is an integer, while the other is a fraction as it's 1/2.

That's what you can't get with algebraic integers.

So

2x^2 - 5x + 1 = 0

can't have an algebraic integer root, so mathematicians decided you can't have a pairing like I just showed you, but they were wrong.

It's that simple. They made a mistake that can be explained with some quadratics.

The reality is that non-rationals aren't so different, and a number that is more like 1 than it's like 1/2 can be paired with a number that's more like 1/2 than it's like 1, but not in the ring of algebraic integers.

So if you follow the math and go with what is proven, ideal theory doesn't work, as it's not doing anything. There is none of this class number anything. No ideals that mean anything.

Nothing to any of that, it's just crap.

Human nature being what it is, people can deny that, and deny all of my research to deny it, deny publication or a dying journal, just like people before you could deny that the world wasn't on the back of elephants, or believe that the sun could be made to stand still by the will of God for some stupid battle of some small group of minor people in a story about something that never actually happened.

You people in denying mathematical proof are no different from people who denied that man landed on the moon. You are no different from Creationists who will argue day and night that the earth was created in six days, or will tell you that soon the end of the world is coming and angels will fly around killing people in God's name.

You people in fighting mathematical proof are no different from any other group of people in the past or present who when faced with a truth they do not like, just decide to ignore the truth, against all facts, against even dramatic happenings, and may even fight to the death for their beliefs.

You are no different.

And for that reason, you are not really mathematicians.