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

- Mar 13th 2012, 07:20 AMmashDo you consider zero to be a whole number? Positive or negative?
Do you consider zero to be a whole number? Positive or negative?

- Mar 13th 2012, 07:50 AMprincepsRe: Do you consider zero to be a whole number? Positive or negative?
- Mar 13th 2012, 07:57 AMPlatoRe: 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 $\displaystyle \emptyset.$ - Mar 20th 2012, 05:55 AMHallsofIvyRe: Do you consider zero to be a whole number? Positive or negative?
And 0 is neither positive nor negative.

- Mar 20th 2012, 06:50 AMProve ItRe: Do you consider zero to be a whole number? Positive or negative?
- Mar 24th 2012, 07:05 AMcshanholtzerRe: 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.

- Mar 24th 2012, 09:03 AMthm43608Re: 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. - Mar 24th 2012, 10:13 AMPlatoRe: Do you consider zero to be a whole number? Positive or negative?
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. - Mar 24th 2012, 11:54 AMthm43608Re: Do you consider zero to be a whole number? Positive or negative?
Ribenboim (1996) states "Let http://mathworld.wolfram.com/images/...er/Inline1.gif be a set of natural numbers; whenever convenient, it may be assumed that http://mathworld.wolfram.com/images/...er/Inline2.gif."

I think that it probably does not matter too much as long as you define the natural numbers first and use the set consistently.