Is zero positive or negative ?

[Jadaav]

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

 

[phinds]

yes, yes, yes

 

[Mark44]

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]

is noon am or pm?

 

[micromass]

Zero is neither positive, neither negative. By definition.

 

[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.

 

[Mark44]

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.

 

[Studiot]

One further comment for discussion.

Is zero odd or even?

 

[micromass]

One further comment for discussion.

Is zero odd or even?

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

 

[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! :]

 

[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...

 

[Mark44]

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).

 

[Studiot]

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.

 

[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.

 

[agentredlum]

That is, we can have 0=ab without a and b invertible...

Non zero divisors of zero

 

[Mark44]

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.

 

[agentredlum]

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.

 

[agentredlum]

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

LOL! How about 12:00 am - dt when dt-->0

 

[ArcanaNoir]

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.

 

[ArcanaNoir]

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]

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.

 

[Jadaav]

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 ?

 

[Jadaav]

Zero in common sense to me means nothing. I think this is obvious to everyone since once your teacher said " Zero is when you have nothing ". The problem to zero is not zero itself but in fact its the concept of nothing.

Long time back, vacuum was considered to be nothing. But now, scientist doesn't agree with that due to the expected presence of Dark Matter and Dark Energy. No one can explain what nothingness really is.

 

[phinds]

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 ?

Don't hijack this thread. If you have a new question, start a new thread.

 

[phinds]

Zero in common sense to me means nothing. I think this is obvious to everyone since once your teacher said " Zero is when you have nothing ". The problem to zero is not zero itself but in fact its the concept of nothing.

.

I don't agree w/ this at all. If you are asked the question what's two minus two, do you say there is no answer? Saying zero is nothing sounds to me like saying that zero is the absence of information and that's not the case.

 

[Jadaav]

OK, I'll start a new thread. But it sounded to be related to this topic to me.

I don't agree w/ this at all. If you are asked the question what's two minus two, do you say there is no answer? Saying zero is nothing sounds to me like saying that zero is the absence of information and that's not the case.

how ? why is it not the absence of information ?

 

[agentredlum]

Zero in common sense to me means nothing. I think this is obvious to everyone since once your teacher said " Zero is when you have nothing ". The problem to zero is not zero itself but in fact its the concept of nothing.

Long time back, vacuum was considered to be nothing. But now, scientist doesn't agree with that due to the expected presence of Dark Matter and Dark Energy. No one can explain what nothingness really is.

Zero can be used to achieve things. Consider x^3 + 1 and add zero in the form of -x + x = 0

x^3 - x + x + 1

x(x^2 - 1) + (x + 1)

x(x - 1)(x + 1) + (x + 1)

(x + 1)[x(x - 1) + 1]

(x + 1)(x^2 - x + 1)

So using zero a factoring is acheived. The interesting thing here is zero split into equal parts, a negative and a positive, and regrouped to accomplish the factoring. This was mentioned in a previous post by phinds as 2 - 2 = 0

There is also the example of destructive interference from wave physics where 2 opposite amplitudes together give darkness.

 

[phinds]

OK, I'll start a new thread. But it sounded to be related to this topic to me.



how ? why is it not the absence of information ?

so if you have a are considering a line segment on the X axis from -3 to +3, are you telling me that there is no meaning to say you are talking about the point at 0 ? If this is so, why would it be meaningful to talk about the point at +2 ? How are they different?

"the answer is zero" and "there is no answer" are not even remotely the same thing and I can't imagine how you can think they are.

 

[Travis_King]

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".

How many million dollar bills do you have in your wallet?

 

[micromass]

How many million dollar bills do you have in your wallet?

She was arguing that there is no time 0. She wasn't talking about dollar bills...

 

[Travis_King]

Ah, though, yea there is. It exists between 23:59.99 and 00:00.01

 

[micromass]

Ah, though, yea there is. It exists between 23:59.99 and 00:00.01

Maybe there isn't something between those two time units??

 

[mariush]

Maybe there isn't something between those two time units??

But is time not continuous?

 

[micromass]

But is time not continuous?

That's the question of course. I don't know the answer. It only doesn't seem obvious to me that time really is continuous...

 

[mariush]

That's the question of course. I don't know the answer. It only doesn't seem obvious to me that time really is continuous...

Definitely a good question. As far as i recall, time is not quantized in the SM, but the gap between 23:59.99 and 00:00.01 would at least be quite huge

 

[Mute]

Definitely a good question. As far as i recall, time is not quantized in the SM, but the gap between 23:59.99 and 00:00.01 would at least be quite huge

Huge? I'd say the gap between 23:59.99 and 00:00.01 would be no more than 0.02 seconds. That seems pretty small! That's only 3.33 x 10^(-4) minutes. Worse yet, it's only ~5.56x10^(-6) hours! Then again, it's also 2x10^(22) yoctoseconds... Hmmm...

 

[Anonymous217]

Is zero purely real? Purely imaginary? Or both?

I think that depends on the set you're talking about, which can't be extended to a general sense (as the question asks). In R, it's purely real. In C, it's both. Not sure if there's a field of solely iR, but that's just isomorphic to R. You're basically asking what the identity element represents for all modules (or some other set).

 

[Mentallic]

Huge? I'd say the gap between 23:59.99 and 00:00.01 would be no more than 0.02 seconds. That seems pretty small! That's only 3.33 x 10^(-4) minutes. Worse yet, it's only ~5.56x10^(-6) hours! Then again, it's also 2x10^(22) yoctoseconds... Hmmm...

Or even 3.7x10⁴¹ Planck times! I have a feeling this is why the mention of continuity in real life has been approached with caution.

 

[Travis_King]

Considering the fact that our quantization of "Time of day" is essentially just convenient, regardless of how you define your timesteps, if 23:59.99 is your cutoff, and exceeding that will reset the clock to 00:00, then there exists a point in time where our "time of day" is zero.

If you are resetting a couting cycle, there is at least one point (in whatever scale you use) in which the value is zero.

 

[SteveL27]

Considering the fact that our quantization of "Time of day" is essentially just convenient, regardless of how you define your timesteps, if 23:59.99 is your cutoff, and exceeding that will reset the clock to 00:00, then there exists a point in time where our "time of day" is zero.

Only if you believe time is continuous. Do we have any evidence for that?

This thread seems to be confusing math with physics.

 

[mariush]

Only if you believe time is continuous. Do we have any evidence for that?

This thread seems to be confusing math with physics.

Does not the time of day question rely (for any practical aspect) on in what intervals we count time?

 

[Travis_King]

Only if you believe time is continuous. Do we have any evidence for that?

This thread seems to be confusing math with physics.

Well, the thread started as a math question. Zero exists mathematically. It certainly exists practically.

And whether or not time is continuous is irellevent to the "time of day" question. Within the system of "time of day", time is continuous and measurable. Therefore, within that system, zero exists.

 

[micromass]

Within the system of "time of day", time is continuous and measurable.

Proof please?

 

[Travis_King]

Proof please?

It's true by definition. Our measurement of "time of day" presupposes that time is continuous. If we are talking about that system, we are working with all of its presuppositions. For example, we can meaningfully discuss the existence of fairies in fairy tales, because that system, "Fairy tales", allows or even presupposes their existence. If we are talking about fairy tales, I wouldn't ask for a proof of the existence of fairies outside the realm of fairy tales.

The same goes for this. Argue that our system of time measurement is wrong/invalid/what-have-you all you want, but while we are talking about our time of day issue, we ought to stick to the rules that define it.

/end pedantic sounding rant

 

[agentredlum]

I think that depends on the set you're talking about, which can't be extended to a general sense (as the question asks). In R, it's purely real. In C, it's both. Not sure if there's a field of solely iR, but that's just isomorphic to R. You're basically asking what the identity element represents for all modules (or some other set).

If you approach zero on the real axis then it's puely real, although it's negative on the left and positive on the right.

If you approach zero on the imaginary axis, then it's purely imaginary, negative on the bottom and positive on top.

These are not the only ways to approach zero in the complex plane. If you approach zero in any other way then it is neither purely real, nor purely imaginary. You also lose the notion of positive or negative.

So, can we say that in the complex plane zero is both and neither but depends on how you approach zero?

 

[Galron]

It depends how you want to render your axioms, generally though it is neither.

One further comment for discussion.

Is zero odd or even?

Is your mum odd or even.

By which I mean this implies a category error by definition. Nothing is neither or no thing or zero is neither. Is everything odd or even?

In early maths or at least post classical math there were two concepts one was Om of the Atman or everything and one was nothing, The Indians denoted nothing with 0 and everything with ∞ or at least with the term infinity/all that is and can be.

 

[Mark44]

I think that depends on the set you're talking about, which can't be extended to a general sense (as the question asks). In R, it's purely real. In C, it's both. Not sure if there's a field of solely iR, but that's just isomorphic to R. You're basically asking what the identity element represents for all modules (or some other set).

If you approach zero on the real axis then it's puely real, although it's negative on the left and positive on the right.

Does "it" in your sentence refer to the same thing? If so, zero is neither positive nor negative.

If you approach zero on the imaginary axis, then it's purely imaginary, negative on the bottom and positive on top.

Like Anonymous217 said, it depends on which zero you're talking about. Zero in the reals is different from zero in the complex numbers.

These are not the only ways to approach zero in the complex plane. If you approach zero in any other way then it is neither purely real, nor purely imaginary. You also lose the notion of positive or negative.

So, can we say that in the complex plane zero is both and neither but depends on how you approach zero?

Both real and imaginary AND neither real nor imaginary?