# Is zero positive or negative ?

1. Aug 31, 2011

Is Zero a positive or negative whole number ? Is it even a whole number ?

2. Aug 31, 2011

### phinds

yes, yes, yes

3. Aug 31, 2011

### Staff: Mentor

I disagree with the first two answers. A positive number is one that is greater than zero. A negative number is one that is less than zero.

From wikipedia (http://en.wikipedia.org/wiki/Positive_number)

4. Aug 31, 2011

### mathwonk

is noon am or pm?

5. Aug 31, 2011

### micromass

Zero is neither positive, neither negative. By definition.

6. Aug 31, 2011

### phinds

OK, I may be splitting hairs and NOT have the correct defintion. I'm an engineer and what I care about is that I've noticed that I can use 0, +0, and -0 indiscriminately in any equation, so to us engineers, they're all the same.

7. Aug 31, 2011

### Staff: Mentor

Here's some more from the same wiki source.

8. Aug 31, 2011

### Studiot

One further comment for discussion.

Is zero odd or even?

9. Aug 31, 2011

### micromass

Even. There is an integer x such that 0=2x.

10. Aug 31, 2011

### Anonymous217

0 being neither positive nor negative follows from the definition of positive and negative.
0 being even and not odd follows from the definition of even and odd.

So what's the lesson? Follow the definitions! :]

11. Aug 31, 2011

### micromass

More interesting discussion: is 0 prime?

Of course, if we follow the definition, then 0 is not a prime number. It's easy as that. But there are some reasons why we should look at 0 as a prime. For example, it satisfies

$$p~\vert~ab~~ \Rightarrow ~~p~\vert~a~~\text{or}~~p~\vert~b$$

Furthermore, (0) is a prime ideal (in $\mathbb{Z}$).

On the other hand, 0 is not irreducible. That is, we can have 0=ab without a and b invertible...

12. Aug 31, 2011

### Staff: Mentor

I don't think anyone picked up on this. Noon is neither AM (ante meridiem = before noon) nor PM (post meridiem = after noon). So technically, the time should be written as 12:00 noon, not 12:00AM or 12:00PM.

Same with midnight.

13. Aug 31, 2011

### olivermsun

I'm willing to bet that 12:00AM and 12:00PM will be strictly correct whenever you see them displayed (provided the clock is showing the right time, of course).

14. Aug 31, 2011

### Studiot

This used to be the old way to denote 1200 - 12 noon or 12 midnight.

To extend the odd / even discussion

0 fulfils the requirement the between every two odd integers there is at least one even one.

15. Aug 31, 2011

### agentredlum

Is zero purely real? Purely imaginary? Or both?

About 12:00 am and 12:00 pm, both notations follow the arrow of time so there is nothing wrong with them.

16. Aug 31, 2011

### agentredlum

Non zero divisors of zero

17. Aug 31, 2011

### Staff: Mentor

What do they have to do with the arrow of time?

In any case, going by the literal definitions of AM and PM, which translate to "before noon" and "after noon" respectively, it doesn't make sense to write 12:00 AM or 12:00 PM. That's not to say that you won't see these all over the place.

18. Aug 31, 2011

### olivermsun

Depends if you expect your guests to be late or early for an appointment, I guess...

But like I said earlier, I'm very sure that it will be strictly correct (following your definition) whenever it is seen displayed "in real time," e.g., on a clock.

19. Aug 31, 2011

### agentredlum

One must begin a new day somewhen, even if it is in the middle of the night.

20. Aug 31, 2011

### olivermsun

Ah, but then one must also end the previous day somewhen.