"0 is neither positive nor negative."
I know that this is probably trivial for all of you, but I'm having a little trouble figuring it out. This is what I wrote down, but I'm not too sure that it's correct:
-0 = 0
-0 + 0 = 0 + 0
0 = 0
Therefore -0 = 0
Is this correct or am I missing something?
Those ARE ring axioms, which means they are facts you can use whenever working with rings.
Axioms are axioms for a reason. Generally, if they could be proven as theorems from the other axioms, then they wouldn't BE axioms.