Do you consider zero to be a whole number? Positive or negative?
There is no universal agreement on the answer to that question.
The term whole number was coined by the mathematics education community denote the set This due to the troubled history of zero. So they call the set the natural numbers.
In my view, most working mathematicians include 0 in the set of natural numbers due to the fact that we start with 0 being identified with
I consider zero to be a whole number but not a natural number. Generally when I am wanting to say that is a whole number, I say . My professors and advisor seem to agree with me on this.
Also, I consider zero to be neither positive nor negative. However, it is an even number.
Several replies have agreed with this point-of-view.
I would ask to be shown a widely used set theory textbook that does not include zero as a natural number.
I know of only two minor texts that do not.
Peano originally began his axioms on natural numbers with 0.
Hilbert adopted that convention even though Dedekind very much disagreed.
Ribenboim (1996) states "Let be a set of natural numbers; whenever convenient, it may be assumed that ."
I think that it probably does not matter too much as long as you define the natural numbers first and use the set consistently.