Negative Zero

Yes, it is a real number.

Every once in a while, I find students who show surprise or disbelief when they first encounter the concept of -0 (negative zero).
Let's say they are solving some equation, and close to the end it reads like x = - (a - b), where a and b represent two numbers known to be equal by virtue of the conditions set at the beginning of the problem.
So, in this example, the next step would be to write x = - 0.
My observation here is that, some students in this situation freeze, turn their head towards me, with a strange look in their face, and go: "There is no negative zero, is there?"
Usually I reply: "Why not?"
And they go: "But ..., what is it?"
I say: "It's zero."
Then they say: "Oh! Really? Just that, zero? Are they the same?"
And I say: "Yes, they are the same thing."
And they go: "O.K."
They seem to suddenly realize that the concept makes sense and it's not really that big of a deal.
I mean, what else could it be? What else could negative zero be if it wasn't equal to zero? There is no other option.
Actually, being equal to its own negative, is a defining feature that uniquely identifies zero.
Zero is the only number equal to its own negative. If you find any number x for which x = - x holds true, then you know x must be zero.
However, the momentary puzzlement, surprise and disbelief some students show when confronting this concept for the first time, is quite natural.
Remember it took centuries for Western civilization to come in contact with the concept of zero, and to fully adopt it as part of the number family. At first it was not considered a "true" number, but only an artificial placeholder used in the representation of "true" numbers.
Not only zero had difficulties being accepted as a number, but also the number One went through a period in Greek history when it was considered more like a philosophical, psychological, or even a religious concept, not a plain mathematical entity.