Is zero positive or negative ?

[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?

 

[Anonymous217]

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?

That's being too vague on your definition. As I said, it depends moreover on how you define your set which contains 0. Any approach to zero in the complex plane approaches 0 = a + bi = 0 + 0i, which is 0 in the real and 0 in the complex. Or you could consider C as R^2, so 0 in C is just (0,0) in R^2. In R^2, (0,0) is "purely real". However in C, 0 is "both imaginary and real". So even if you're considering two isomorphic structures, what the element actually means depends on what the structure is.

This is your equivalent question: "What does the identity element represent in set-theoretic terms for any set containing it?" However, this can't be answered because first of all, it's not even possible to generalize what the identity element represents, since what it represents depends on the set you're discussing. In one set, the identity could be "purely real" and in another, the identity could be "purely bananas".

 

[agentredlum]

Does "it" in your sentence refer to the same thing? If so, zero is neither positive nor negative.Like Anonymous217 said, it depends on which zero you're talking about. Zero in the reals is different from zero in the complex numbers.
Both real and imaginary AND neither real nor imaginary?

That's being too vague on your definition. As I said, it depends moreover on how you define your set which contains 0. Any approach to zero in the complex plane approaches 0 = a + bi = 0 + 0i, which is 0 in the real and 0 in the complex. Or you could consider C as R^2, so 0 in C is just (0,0) in R^2. In R^2, (0,0) is "purely real". However in C, 0 is "both imaginary and real". So even if you're considering two isomorphic structures, what the element actually means depends on what the structure is.

This is your equivalent question: "What does the identity element represent in set-theoretic terms for any set containing it?" However, this can't be answered because first of all, it's not even possible to generalize what the identity element represents, since what it represents depends on the set you're discussing. In one set, the identity could be "purely real" and in another, the identity could be "purely bananas".

Well, let's just consider the real number line for now. If I want to discover whether zero is positive or negative, is it wrong to consider other numbers close to zero?

AFAIK zero is neither positive nor negative by definition. A definition that disregards the evidence.

Now let's consider the complex plane. Is it wrong to try to discover features of zero by considering features of other numbers in the neighborhood of zero?

Clearly not, as this is done all the time, numbers are explained by other numbers very close to them.

 

[SteveL27]

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?

0 is real, because its imaginary part is zero; and its imaginary, because its real part is zero. Nothing to do with how you approach it. It's 0 + 0i regardless.

 

[agentredlum]

0 is real, because its imaginary part is zero; and its imaginary, because its real part is zero.

I don't have a problem with zero being both, the way I like to understand, it is because zero is at the intersection of the axes in the complex plane.

I'm just thinking here, if you approach zero on a straight line 45º to the positive real axis, then you stay away from both axes. Think of zooming in, the picture looks the same. So you can reach zero by AVOIDING all purely real and all purely imaginary numbers.

Of course there are many other ways to approach zero.

 

[Travis_King]

1: Zero is neither positive nor negative BY DEFINITION
2: Zero has both real and imaginary parts, just like all numbers. But like real integers, it's imaginary component is zero. The question is semantical and nonsensical.

 

[Anonymous217]

This is going to be my third time repeating it, but it depends on the set you're discussing. If you consider the complex numbers as your set, then ALL real numbers have both a real and imaginary part. That is, for x in R<C, x=x + 0i.

However, considering the reals as your set, then ALL real numbers have only a real part. That is, for x in R, x=x. That's it, and zero is only a specific case for x. It doesn't matter how you approach it; we're defining the set to be something, and so all elements are part of that 'something'. Shouldn't be too hard to understand..

 

[agentredlum]

1: Zero is neither positive nor negative BY DEFINITION
2: Zero has both real and imaginary parts, just like all numbers. But like real integers, it's imaginary component is zero. The question is semantical and nonsensical.

Ah-hmmmm...

x = -x has solution 0

substitute back

0 = -0 (result1)

x = -x has solution -0

-0 = -(-0)

-0 = 0

same as (result1)

-0 = 0 = +0

all 3 are equal

to say zero has no sign disregards evidence and is purely by convention, not by truth or proof.

 

[Travis_King]

Yea. What's -0 + -0?
What's +0 + (+0)?
There is no meaning to a sign as it applies to zero. Because zero is neither on the plus nor minus size of zero. It is zero.

The only time you would ever use a signed zero is to say "We are going to take this value as zero, but keep in mind that it is really an extremely small negative number rounded to zero. It's use is merely practical, and your "proof" merely demonstrates that you can use a signed zero without any real problems--basically because, well, IT IS ZERO lol

edit: and just so we are clear. By practical, I mean I understand that it has implications as far as math goes (i.e. 1/+0 should be +inf and 1/-0 should be -inf) but it is only because we are taking the signed zero as a simplistic way of representing impossibly small numbers on either side of the number line and want to maintain sign for computing purposes (say, after an underflow or similar situation)

 

[Jadaav]

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

What's SM ?

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

This thread seems to be confusing math with physics.

Physics just relates everything that's happening in term of maths, so what's the problem.

For time to start or reset at midnight ( by saying ), shouldn't there be a big bang ?

This question now goes back to big bang or at the moment of creation. Time and everything else was produced at big bang so its going to be continuous Or else how would you explain time restarting at that moment ? in fact it wouldn't even be called a moment. With time stopping, everything stops with the notion of time also.

Everything is interlinked, so when 2 things coincide to become a proof. Each one proving the other one.

 

[agentredlum]

Yea. What's -0 + -0?
What's +0 + (+0)?

It is 0 - 0i + 0j - 0k...

It is at the intersection of all co-ordinate axes, whether they be Complex, Quaternions, Octonians, etc.

Hooray!

LOL

 

[SteveL27]

I found this. It's interesting.

An imaginary number is a number with a square that is negative.

http://en.wikipedia.org/wiki/Imaginary_number

By that definition, 0 is not imaginary. I would say that Wiki is wrong. I'd say 0 is imaginary because a) its real part is zero; and b) it lies on the imaginary axis.

Of course this is only a matter of semantics, like "Is 0 a natural number?" But still ... Wiki is usually correct when it comes to technical facts.

Curious to see what people think about this.

 

[agentredlum]

I found this. It's interesting.

An imaginary number is a number with a square that is negative.

http://en.wikipedia.org/wiki/Imaginary_number

By that definition, 0 is not imaginary. I would say that Wiki is wrong. I'd say 0 is imaginary because a) its real part is zero; and b) it lies on the imaginary axis.

Of course this is only a matter of semantics, like "Is 0 a natural number?" But still ... Wiki is usually correct when it comes to technical facts.

Curious to see what people think about this.

The wiki article works if 0 = -0

then (0)^2 = 0

by transitive property (0)^2 = -0

So zero is imaginary because it's square is negative.

LOLOL.

 

[Mark44]

The wiki article works if 0 = -0

then (0)^2 = 0

by transitive property (0)^2 = -0

So zero is imaginary because it's square is negative.

-0, +0, and 0 all represent the same number, which is neither negative nor positive. Merely attaching a sign to 0 does NOT make it either negative or positive.

 

[Mark44]

Ah-hmmmm...

x = -x has solution 0

substitute back

0 = -0 (result1)

x = -x has solution -0

-0 = -(-0)

-0 = 0

same as (result1)

-0 = 0 = +0

all 3 are equal

to say zero has no sign disregards evidence and is purely by convention, not by truth or proof.

No. To say that zero has a sign ignores what you have shown here. Since -0 = 0 = +0, that should convince you that a sign on zero is irrelevant.

Since negative numbers are always smaller than positive numbers, your equation above should read -0 < 0 < +0. I hope that you will agree that this inequality is nonsense.

 

[agentredlum]

No. To say that zero has a sign ignores what you have shown here. Since -0 = 0 = +0, that should convince you that a sign on zero is irrelevant.

Since negative numbers are always smaller than positive numbers, your equation above should read -0 < 0 < +0. I hope that you will agree that this inequality is nonsense.

Yes, the inequality is nonsense. Zero is an exception. It is the only real number equal to it's negatve. You claim negative numbers are always smaller than positive numbers. If zero is not positive or negative, how does your argument above work?

I never said -0 is less than 0 don't know why you think I did...

 

[Mark44]

Yes, the inequality is nonsense. Zero is an exception. It is the only real number equal to it's negatve. You claim negative numbers are always smaller than positive numbers.

And this is not an idle claim. Every negative number is smaller than any positive number. A look at the number line should convince you of this.

If zero is not positive or negative, how does your argument above work?

What argument are you talking about?

I never said -0 is less than 0 don't know why you think I did...

Because you are saying that 0 is negative.

by transitive property (0)^2 = -0
So zero is imaginary because it's square is negative.

When you attach a sign to zero, you are implying that there is some difference between -0, 0, and +0. In some contexts (particularly in floating point number representations in computer science) there are differences, but in mathematics these all represent the same number.

 

[agentredlum]

And this is not an idle claim. Every negative number is smaller than any positive number. A look at the number line should convince you of this.
What argument are you talking about?

Because you are saying that 0 is negative.


When you attach a sign to zero, you are implying that there is some difference between -0, 0, and +0. In some contexts (particularly in floating point number representations in computer science) there are differences, but in mathematics these all represent the same number.

If I thought there was a difference I would not write -0 = 0 = +0

You do not want to accept the idea that a positive number can be equal to a negative number. For real numbers this happens only once, in the case of zero so it does not have any undesirable consequences for other real numbers. Why is the idea so offensive?

 

[micromass]

Why is the idea so offensive?

Because it's not true by definition.
What would be a benefit if 0 was considered positive and negative?? Is there a benefit?

 

[agentredlum]

Because it's not true by definition.
What would be a benifit if 0 was considered positive and negative?? Is there a benifit?

It makes the wiki article work!

See posts 61 and 62

LOL

 

[micromass]

It makes the wiki article work!

See posts 61 and 62

LOL

No it doesn't. The wiki article implies that 0 is not purely imaginary. I'm pretty sure that is indeed the standard definition.