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

**mash** · March 13th 2012, 07:20 AM

**princeps** · March 13th 2012, 07:50 AM

Zero

**Plato** · March 13th 2012, 07:57 AM

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

**HallsofIvy** · March 20th 2012, 05:55 AM

And 0 is neither positive nor negative.

**Prove It** · March 20th 2012, 06:50 AM

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 $\emptyset.$

I don't. It's not natural to count "nothing", since you can not see "nothing".

**cshanholtzer** · March 24th 2012, 07:05 AM

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

**thm43608** · March 24th 2012, 09:03 AM

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

**Plato** · March 24th 2012, 10:13 AM

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 $x$ is a whole number, I say $x \in \left( \mathbb{N} \cup \{0\} \right)$ . 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.

**thm43608** · March 24th 2012, 11:54 AM

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.

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