You say you have an advanced degree in Math? Fat Chance.....
(THIS is an answer to my proof? Sheesh!)
It is true that writing mathematical symbols arbitrarily in nonsense syntax related to nothing doesn't take a high school education...
So either you're incredibly stupid or you're trolling again....
ETA: Thread re-opened, after PMGrapes' responses have degenerated into childish nonsense and inane propositions empty of any technical or mathematical content. (I suspect it is because he knows I am right and doesn't have the courage or ethics to admit it. But that's ok; my analysis is on my website for the world to see... time will tell...)
c1=g1(a,b) = (Fermat's Expression)
c2=g2(a,b) = (The Binomial Expansion).
Fermat's expression is the integer metric for a Presburger arighmetic (without multiplicative products like
The Binomial Expansion includes Fermat's expression but also those multiplicative products in Rem(a,b,n), and therefore is consistent as a metric for the two dimensional (real number) field (a,b)) with Peano's axioms. However, Fermat's expression requires that a=0 or b=0 for n>2 if c is to be an integer (for fields, division is always possible so is always possible, so the field of positive real numbers is consistent and but not complete (Godel's proof is based on positive integers), since it requires complex numbers for subraction (). The key issue is that one needs two fields (Cartesian coordinates) to define any function y=f(x) at all, not to mention z=g(x,y) as in the Binomial Expansion for z a single valued resultant variable.
Cartesian coordinates can express real numbers without the necessity of Dedekind cuts in a single dimension number line.
STR provides a way of generating continuous fields (without using Dedekind cuts) and for positive fields, also provides trigonometric functions (and negative fields if Dirac is included).
One liner responses from the Peanut Gallery with no intellectual content whatever in responses to posts like this (where I can provide Wiki links as necessary) are merely spam and bloating my thread's intellectual content with nothing other than complaints indicating that the Peanut Gallery have no idea WTF I am talking about.