# Thread: Do you consider zero to be a whole number? Positive or negative?

1. ## Do you consider zero to be a whole number? Positive or negative?

Do you consider zero to be a whole number? Positive or negative?

3. ## Re: Do you consider zero to be a whole number? Positive or negative?

Originally Posted by mash
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 $\displaystyle \{0,1,2,\cdots\}.$ This due to the troubled history of zero. So they call the set $\displaystyle \{1,2,\cdots\}$ 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 $\displaystyle \emptyset.$

4. ## Re: Do you consider zero to be a whole number? Positive or negative?

And 0 is neither positive nor negative.

5. ## Re: Do you consider zero to be a whole number? Positive or negative?

Originally Posted by Plato
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 $\displaystyle \emptyset.$
I don't. It's not natural to count "nothing", since you can not see "nothing".

6. ## Re: Do you consider zero to be a whole number? Positive or negative?

I have only encountered 0 as a natural number in computer science for instance a language theory class.

7. ## Re: Do you consider zero to be a whole number? Positive or negative?

I consider zero to be a whole number but not a natural number. Generally when I am wanting to say that $\displaystyle x$ is a whole number, I say $\displaystyle x \in \left( \mathbb{N} \cup \{0\} \right)$. 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.

8. ## Re: Do you consider zero to be a whole number? Positive or negative?

Originally Posted by thm43608
I consider zero to be a whole number but not a natural number. Generally when I am wanting to say that $\displaystyle x$ is a whole number, I say $\displaystyle x \in \left( \mathbb{N} \cup \{0\} \right)$. My professors and advisor seem to agree with me on this.
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.

9. ## Re: Do you consider zero to be a whole number? Positive or negative?

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.