10998521 has the definition of nonnegative correct... however, the opposite of nonnegative is negative. The prefix non- means opposite.
Consider: a real number is either nonnegative or the opposite of nonnegative, and not both. (By any reasonable definition of opposite, something cannot be both A and the opposite of A at the same time.) Zero is, by definition, a nonnegative number. So zero is not the opposite of nonnegative, and zero is nonpositive (by definition again), so nonpositive is not the opposite of nonnegative.