"0 is neither positive nor negative."
from http://en.wikipedia.org/wiki/0_(number)
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?
"0 is neither positive nor negative."
from http://en.wikipedia.org/wiki/0_(number)
Surprised you couldn't look this one up on your own!
PlanetMath: zero times an element is zero in a ring
Of course if you are allowed to redefine things the way you want, you can prove ANYTHING.
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.