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

• March 13th 2012, 07:20 AM
mash
Do you consider zero to be a whole number? Positive or negative?
Do you consider zero to be a whole number? Positive or negative?
• March 13th 2012, 07:50 AM
princeps
Re: Do you consider zero to be a whole number? Positive or negative?
• March 13th 2012, 07:57 AM
Plato
Re: Do you consider zero to be a whole number? Positive or negative?
Quote:

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 $\emptyset.$
• March 20th 2012, 05:55 AM
HallsofIvy
Re: Do you consider zero to be a whole number? Positive or negative?
And 0 is neither positive nor negative.
• March 20th 2012, 06:50 AM
Prove It
Re: Do you consider zero to be a whole number? Positive or negative?
Quote:

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".
• March 24th 2012, 07:05 AM
cshanholtzer
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.
• March 24th 2012, 09:03 AM
thm43608
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 $x$ 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.
• March 24th 2012, 10:13 AM
Plato
Re: Do you consider zero to be a whole number? Positive or negative?
Quote:

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.
• March 24th 2012, 11:54 AM
thm43608
Re: 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.