Does excluding or including zero from the definitions of "positive" and "negative" make any consequential difference in mathematics? I was absolutely certain that zero was both positive and negative. And zero was neither strictly positive nor strictly negative.
But today I made a few Google searches, and they all say the same thing: zero is neither positive nor negative.
I suppose that the definition of "positive" and "negative" depend on which country we're living in. In the U.S. "positive" and "negative" exclude zero. In France "positive" and "negative" include zero.
My question therefore is: does excluding or including zero from the definitions of "positive" and "negative" make any consequential difference in mathematics?

Injecting a little chauvinism just for fun:
Positive and negative, maybe the French are simply wrong. Consider $\Bbb N$, the set of natural numbers. English-speaking mathematicians do disagree on whether or not $0\in\Bbb N$. And that disagreement has no mathematical consequences whatever.
