It sais perfectly clear that minus zero does not exist, when you combine it with the axiom of identity.
It would be better for you if you avoided this pseudo-rigorous, "math-guy", jargon nonsense. If you really want a formal approach, look up the
additive inverse axiom (
here's one link,
here's another). In short, the additive inverse is defined for
every element in an
additive group. Now the additive inverse of a number A is
commonly written as -A. Thus -0 is the additive inverse of 0.
That does not mean -0 is distinct from 0, which is essentially what Wikipedia is saying, and what you keep misinterpreting: -0 does not exist
as distinct from 0. Notice the italics: they are part of the sentence and not something for you to ignore. Wikipedia even included the equalities -0 = +0 = 0, which you also conveniently ignored. If the author thought -0 was invalid/undefined, (s)he wouldn't use it in a mathematical expression.
You cannot have two symbols that represent the same concept.
So is +5 incorrect too? +5 and 5 both represent the same thing. How about sqrt(1)? That represents the same concept as 1.
This means that when you shall give a final answer to a mathematically question you can never say minus zero. If you do, you have given an answer that is not correct, presumptive an answer that is not completely reduced.
So now you're saying that the actual problem is that the answer is not reduced (although the non-reduced answer is valid mathematically)? Which is it? Is the answer correct but merely not reduced or is it flat out incorrect?
