Harristotelian Logic

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-factorization-paper

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, 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.

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