Bob, an "axiom" in one system may be a "corrolary" or a "theorem" in another. I think you are mistaken to say that I attempt to prove axioms. What I am trying to do is to make judicious choices concerning axioms, and then proving certain theorems or corrolaries based on that choice. In the case of negative numbers, I don't believe it is an axiom that -1 x -1 = 1, but perhaps it could be in a particular system.
