Harristotelian Logic

Assume I'm correct in that from the ring of objects you can prove that units are being used in the ring of algebraic integers where they are not units to wrap up constants like 7 so that you can divide them off and remain in that ring.

Then you find a consistent argument as I've stated.

For those who don't know I have the following definition for the ring of objects:

The object ring is defined by two conditions, and includes all numbers such that these conditions are true:

1. 1 and -1 are the only rationals that are units in the ring.


2. Given a member m of the ring there must exist a non-zero member n such that mn is an integer, and if mn is not a factor of m, then n cannot be a unit in the ring.

(I'll note that there has been some disagreement from others about the necessity of the second condition.)

The ring of algebraic integers is included in the object ring while numbers like 1/2, 1/3, or 1/sqrt(2) are excluded.

>From the ring of objects my Wrapper theorem (shown at my math blog) shows how you can appear to divide off integers within the ring of algebraic integers in what I call non-polynomial factorizations by multiplying with units in the ring of objects that are NOT units in the ring of algebraic integers. I call those numbers wrappers.

There is no mathematical argument blocking that scenario.