On Sunday, September 24, 2017 at 7:47:27 AM UTC-7, Conway wrote:
> [A]n AXIOM by definition can NOT be proven. It is by definition a self inherent truth.
No. In mathematics an axiom is merely a working hypotheses, a "mathematical statement that serves as a starting point from which other statements are logically derived." https://en.wikipedia.org/wiki/Axiom
Any coherent mathematical statement (or it's converse) may be taken as an axiom. Of course, having "made it happen", you must then honestly "deal with the consequences", per James Tanton http://gdaymath.com/about/
As I see it, YOU have two problems. You haven't been able to express your ideas coherently (and lash out at anyone and everyone making an attempt to clarify), and you aren't willing to deal with the (mathematical) consequences-- for instance, that if you can divide by 0 then you haven't got a field.