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

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

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yes, yes, yes

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Mark44

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

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.yes, yes, yes

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

The number zero is neither positive or negative, and therefore has no sign.

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mathwonk

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is noon am or pm?

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Zero is neither positive, neither negative. By definition.

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Mark44

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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.

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One further comment for discussion.

Is zero odd or even?

Is zero odd or even?

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Even. There is an integer x such that 0=2x.One further comment for discussion.

Is zero odd or even?

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0 being even and not odd follows from the definition of even and odd.

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

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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

[tex]p~\vert~ab~~ \Rightarrow ~~p~\vert~a~~\text{or}~~p~\vert~b[/tex]

Furthermore, (0) is a prime ideal (in [itex]\mathbb{Z}[/itex]).

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

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Mark44

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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.is noon am or pm?

Same with midnight.

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olivermsun

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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.

Same with midnight.

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

To extend the odd / even discussion

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

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

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

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Mark44

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What do they have to do with the arrow of time?About 12:00 am and 12:00 pm, both notations follow the arrow of time so there is nothing wrong with them.

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.

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olivermsun

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

But like I said earlier, I'mThat's not to say that you won't see these all over the place.

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

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olivermsun

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Ah, but then one must alsoOne must begin a new day somewhen, even if it is in the middle of the night.

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

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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.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.

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Mark44

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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.But it is 12:00 for a whole minute, that's an infinity longer than the infinitesimal moment of transition between ante/post meridian.

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.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.

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.

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