>It shouldn't have taken you a full page to disprove A = -A. Consider: A +
>-A is zero, or should be. But if A = -A, then A + -A = A + A = 0. You
>could do this for any number, including a constant; all numbers would
>equal zero, including such important numbers as pi and e and 1 and
>infinity, and the probability that anything exists at a given point. In other
>words, you get a nonsense universe.
Completely correct. I am no philosopher or mathematician, but a mere
engineer. However, I was consciously attempting to make the proof more
general, as the above only applies to certain sets of rings and fields. In
addition, you are making the error of equating the operator '-' with 'not'.