# Is zero positive or negative ?

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

phinds
Gold Member
yes, yes, yes

Mark44
Mentor
Is Zero a positive or negative whole number ? Is it even a whole number ?
yes, yes, yes
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)
The number zero is neither positive or negative, and therefore has no sign.

mathwonk
Homework Helper
2020 Award
is noon am or pm?

Zero is neither positive, neither negative. By definition.

phinds
Gold Member
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.

Mark44
Mentor
Here's some more from the same wiki source.
In arithmetic, +0 and −0 both denote the same number 0, and the negation of zero is zero itself.

In some contexts, such as signed number representations in computing, it makes sense to consider signed versions of zero, with positive zero and negative zero being different numbers (see signed zero).

One also sees +0 and -0 in calculus and mathematical analysis when evaluating certain limits. This notation refers to the behaviour of a function as the input variable approaches 0 from positive or negative values respectively; these behaviours are not necessarily the same.

One further comment for discussion.

Is zero odd or even?

One further comment for discussion.

Is zero odd or even?
Even. There is an integer x such that 0=2x.

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! :]

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...

Mark44
Mentor
is noon am or pm?
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.

olivermsun
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.
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).

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.
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.

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.

That is, we can have 0=ab without a and b invertible...
Non zero divisors of zero

Mark44
Mentor
About 12:00 am and 12:00 pm, both notations follow the arrow of time so there is nothing wrong with them.
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.

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

That's not to say that you won't see these all over the place.
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.

What do they have to do with the arrow of time?
One must begin a new day somewhen, even if it is in the middle of the night.

olivermsun
One must begin a new day somewhen, even if it is in the middle of the night.
Ah, but then one must also end the previous day somewhen.

Ah, but then one must also end the previous day somewhen.
LOL! How about 12:00 am - dt when dt-->0

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.
But it is 12:00 for a whole minute, that's an infinity longer than the infinitesimal moment of transition between ante/post meridian. 12:00:01 is already am or pm justifiably. as is 12:00:00:00......:01 to a point where your clock could withhold the am/pm specification for the briefest moment and then display am or pm, and your eyes could never tell that it hesitated.

It's equally incorrect to argue that there's some moment between December 31 and January 1 where we can't say it's either last year or next year. I don't think that moment exists, I think our time measurement dictates that the one ends precisely when the other begins. There is no "0".

Mark44
Mentor
But it is 12:00 for a whole minute, that's an infinity longer than the infinitesimal moment of transition between ante/post meridian.
Well, a digital clock will display 12:00 for a whole minute, but the transition to 12:01 takes a minute, which is only a tad less than a minute longer than the moment of transition you mentioned, and considerably less than an infinity longer.
12:00:01 is already am or pm justifiably. as is 12:00:00:00......:01 to a point where your clock could withhold the am/pm specification for the briefest moment and then display am or pm, and your eyes could never tell that it hesitated.
I'm not thinking in terms of a digital clock that displays each time for one whole minute. I'm thinking more theoretically, and in terms similar to the number line. There is a place on the number line that is ***exactly*** 12 units to the right of 0. If you move slightly to the right, you aren't still at 12, and if you move slightly to the left, you aren't at 11 either.

My point is that it's 12:00 noon only for the briefest instant. After that, it's afternoon.

The Chicago Manual of Style, 13th Ed., uses M. (meridies) for noon, as in 12:00 M. They don't give anything to use for midnight.

More wikipedia (http://en.wikipedia.org/wiki/Noon)
Digital clocks and computers commonly display 12 p.m. for noon. While that phrase may be used practically, it helps to understand that any particular time is actually an instant. The "p.m." shown on clock displays refers to the 12-hour period following the instant of noon, not to the instant itself.

While computers and digital clocks display "12:00 a.m." and "12:00 p.m." these notations provide no clear and unambiguous way to distinguish between midnight and noon. It is actually improper to use "a.m." and "p.m." when referring to 12:00. The abbreviation a.m. stands for ante meridiem (or before the meridian) and p.m. stands for post meridiem (or after the meridian), with the meridian being 12:00 noon. For this reason, neither abbreviation is correct for noon or midnight.[4] The length of the error is determined by the smallest unit of time: 12:00:01 p.m. would be correctly notated, as would even 12:00:00.00001 pm.

I got another question now after reading the previous posts :

How did they started to measure time accurately ? I mean how did they knew if it was midnight today or tomorrow morning ?