## Negative Zero

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### Negative Zero

Zero is used as both referring to the lack of numbers, but it is also the base placeholder.

Negative zero is every number including zero
Ecmandu
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### Re: Negative Zero

I never heard of that, but I've seen -0 mean "to the left of zero" and +0 meaning "to the right of zero" which is the smallest infinitesimal representationally possible.
Serendipper
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### Re: Negative Zero

Nothing from nothing ain't nothing in Wonderland, ya gotta have something, if ya wanna dance!

That expresses the noncommutative nature of quantum mechanics.
wuliheron

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### Re: Negative Zero

Ecmandu wrote:Zero is used as both referring to the lack of numbers, but it is also the base placeholder.

Negative zero is every number including zero

That would be non-zero, as in the set of non-zero numbers.
Karpel Tunnel
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### Re: Negative Zero

Seems useful.

1/+0= +infinity

1/-0= -infinity

It's been a while and I was never that great at calc but for f(x)=1/x as x->-0, f(x)-> -infinity and as x->+0, f(x)-> +infinity

That describes the graph of f(x)=1/x pretty well to me.

Xunzian
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### Re: Negative Zero

Serendipper wrote:I never heard of that, but I've seen -0 mean "to the left of zero" and +0 meaning "to the right of zero" which is the smallest infinitesimal representationally possible.

There could be no such thing. In the standard real numbers there are no infinitesimals and there is no smallest positive real. The proof is that if you tell me x is the smallest positive real, then x/2 is a positive real that's smaller.

But suppose you say, well I've heard of the hyperreals and nonstandard analysis, in which you can do calculus but there are genuine infinitesimals. What about that? It's true that there are systems with infinitesimals. But there is no smallest positive infinitesimal, and the proof I already gave for the real number case works in the nonstandard case too. That's because you can always divide an infinitesimal in half.

So there is no smallest positive infinitesimal even in number systems that have infinitesimals.
wtf

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### Re: Negative Zero

The opposite of no numbers (zero) is every number.
Thus, negative zero is the reals in totality.
Ecmandu
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### Re: Negative Zero

Ecmandu wrote:Zero is used as both referring to the lack of numbers, but it is also the base placeholder.

Negative zero is every number including zero

Technically that would be the "NOT" operator rather than the negative operator.

If we use the symbol "!" to denote "NOT", like in the C language, and we define 0 as "!n" (a lack of numbers/no numbers), where n is any number, then !(!n) would revert to "n": any number.

But is "negative" actually the same as "NOT"? Well, -1 doesn't mean "not 1", it just means 1 less rather than 1 more (+1), so I'd say the proposal is invalid.

Xunzian wrote:1/+0= +infinity

1/-0= -infinity

It's been a while and I was never that great at calc but for f(x)=1/x as x->-0, f(x)-> -infinity and as x->+0, f(x)-> +infinity

That describes the graph of f(x)=1/x pretty well to me.

1/0 isn't infinity, it's undefinable.

The idea that it's infinity presumably comes from any number being divided by smaller and smaller numbers equaling higher and higher numbers that tend towards infinity.

However, consider n/n. Something divided by itself always seems to equal 1, but if n=0, then do we follow the n/0 = infinity rule or the n/n = 1 rule?

Silhouette
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### Re: Negative Zero

Silhouette wrote:
Ecmandu wrote:Zero is used as both referring to the lack of numbers, but it is also the base placeholder.

Negative zero is every number including zero

Technically that would be the "NOT" operator rather than the negative operator.

If we use the symbol "!" to denote "NOT", like in the C language, and we define 0 as "!n" (a lack of numbers/no numbers), where n is any number, then !(!n) would revert to "n": any number.

But is "negative" actually the same as "NOT"? Well, -1 doesn't mean "not 1", it just means 1 less rather than 1 more (+1), so I'd say the proposal is invalid.

Xunzian wrote:1/+0= +infinity

1/-0= -infinity

It's been a while and I was never that great at calc but for f(x)=1/x as x->-0, f(x)-> -infinity and as x->+0, f(x)-> +infinity

That describes the graph of f(x)=1/x pretty well to me.

1/0 isn't infinity, it's undefinable.

The idea that it's infinity presumably comes from any number being divided by smaller and smaller numbers equaling higher and higher numbers that tend towards infinity.

However, consider n/n. Something divided by itself always seems to equal 1, but if n=0, then do we follow the n/0 = infinity rule or the n/n = 1 rule?

So you're splitting hairs between NOT and the OPPOSITE OF...

Not a beaver is a lion for example

The opposite of a beaver is no beavers, negative, lack of, beavers.

In order to postulate a lack of beavers, they already exist in some way. So in NOT a beaver, anything that exists besides a beaver works. Such as a lion.

A lion is a negative zero in this example, as are all NOT beavers. Now the opposite of beavers is no beavers ... but as all the beavers are gone, there are still existents, namely all non beavers, which is the opposite of a beaver.
Ecmandu
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### Re: Negative Zero

Ecmandu wrote:So you're splitting hairs between NOT and the OPPOSITE OF...

Yeah, I already addressed this as a mathematical definite (not just "splitting hairs") here:

Silhouette wrote:But is "negative" actually the same as "NOT"? Well, -1 doesn't mean "not 1", it just means 1 less rather than 1 more (+1), so I'd say the proposal is invalid.

I mean, even with beavers and lions, a "not beaver" can be a lion amongst all other things that aren't beavers, but what really is a negative beaver? The same thing as a not-beaver?

You wanna define negative as a "lack of"? Sure, you can go ahead - in common parlance a "negative" can even mean a no, as in "not what you just said": basically "NOT", and a "lack of" basically means none or NOT (e.g. beavers), such as a lion.

I'm not against you playing around with definitions and seeing what happens, I'm just telling you that mathematically the problem has already been solved by distinguishing NOT and negative e.g. "-1" obviously not being the same as "!1". NOT 1 includes -1 but a whole lot more besides: namely everything else including -1, just not "1". The same can go for beavers and lions, sure...

Not sure I like the suggestion that a lion is a negative zero in your example, because so is a tree, and a lion isn't a tree. At the very least a lion is of the set NOT beaver, of which a tree et al. may also be part. Maybe that's splitting hairs, but distinguishing NOT from negative is not.

Silhouette
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### Re: Negative Zero

Silhouette wrote:
Ecmandu wrote:So you're splitting hairs between NOT and the OPPOSITE OF...

Yeah, I already addressed this as a mathematical definite (not just "splitting hairs") here:

Silhouette wrote:But is "negative" actually the same as "NOT"? Well, -1 doesn't mean "not 1", it just means 1 less rather than 1 more (+1), so I'd say the proposal is invalid.

I mean, even with beavers and lions, a "not beaver" can be a lion amongst all other things that aren't beavers, but what really is a negative beaver? The same thing as a not-beaver?

You wanna define negative as a "lack of"? Sure, you can go ahead - in common parlance a "negative" can even mean a no, as in "not what you just said": basically "NOT", and a "lack of" basically means none or NOT (e.g. beavers), such as a lion.

I'm not against you playing around with definitions and seeing what happens, I'm just telling you that mathematically the problem has already been solved by distinguishing NOT and negative e.g. "-1" obviously not being the same as "!1". NOT 1 includes -1 but a whole lot more besides: namely everything else including -1, just not "1". The same can go for beavers and lions, sure...

Not sure I like the suggestion that a lion is a negative zero in your example, because so is a tree, and a lion isn't a tree. At the very least a lion is of the set NOT beaver, of which a tree et al. may also be part. Maybe that's splitting hairs, but distinguishing NOT from negative is not.

Negative = opposite of

Not = everything but

We are splitting hairs here when these two concepts converge in the special case of zero.
Ecmandu
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### Re: Negative Zero

Ecmandu wrote:Negative = opposite of

Not = everything but

We are splitting hairs here when these two concepts converge in the special case of zero.

Well I'm honoured to have such an in-depth and mutually, life-changingly self-questioning conversation with you. Inspiring.

Silhouette
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### Re: Negative Zero

Silhouette wrote:
Ecmandu wrote:Negative = opposite of

Not = everything but

We are splitting hairs here when these two concepts converge in the special case of zero.

Well I'm honoured to have such an in-depth and mutually, life-changingly self-questioning conversation with you. Inspiring.

I gave you a perfect answer, and you gave me an insult. You know what I think about all you "doth protest too much" subjectivists??? I think you've done some horrible shit, and are trying to claw as hard as you can to avoid falling into the hell you see before your eyes ... maybe if nothing is true, you can get off on a technicality HA!!!

The more you try, the deeper the hole you dig...
Ecmandu
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### Re: Negative Zero

Ecmandu wrote:
Silhouette wrote:
Ecmandu wrote:Negative = opposite of

Not = everything but

We are splitting hairs here when these two concepts converge in the special case of zero.

Well I'm honoured to have such an in-depth and mutually, life-changingly self-questioning conversation with you. Inspiring.

I gave you a perfect answer, and you gave me an insult. You know what I think about all you "doth protest too much" subjectivists??? I think you've done some horrible shit, and are trying to claw as hard as you can to avoid falling into the hell you see before your eyes ... maybe if nothing is true, you can get off on a technicality HA!!!

The more you try, the deeper the hole you dig...

If only hell existed eh?

Then you'd be happy.

But it doesn't Sorry.

You have no capacity to self-evaluate and cannot hear anything other than your own "doth assert too much" objectivist righteousness.

I gave you a logically exhaustive answer, an actual perfect answer. You gave back to me some arbitrary "this oughta mean this, right?" bullshit and call it perfect. What a joke. You're going by colloquial perjoratives to obfuscate the matter when clearer and more critical thinkers already solved your problem. You wish you were creative about something that countless people have already been creative about, to prove to yourself that you're special when you're not. That is the hell you see before your eyes when people like me show you what actually already happened. You think you can fluke your way into the history books on a technicality HA!!!

I was actually being polite to you before, but I see that wasted.

Silhouette
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### Re: Negative Zero

Silhouette wrote:1/0 isn't infinity, it's undefinable.

The idea that it's infinity presumably comes from any number being divided by smaller and smaller numbers equaling higher and higher numbers that tend towards infinity.

However, consider n/n. Something divided by itself always seems to equal 1, but if n=0, then do we follow the n/0 = infinity rule or the n/n = 1 rule?

Such an example presupposes that to divide something by its equal is the same sort of logical operation as to divide it by something different. But I think n/n has no metaphysical bearing on n/p.

The case remains that 0 fits into 1 an infinite amount of times.
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Fixed Cross
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### Re: Negative Zero

Silluoette....

Someone once warned me that mathematics is one of the most mud slinging endeavors you can get into... they get vicious.

Negative zero as I'm expounding it, has existential implications. Zero is space, the placeholder, negative zero is all besides the placeholder.

And actually, I'm not trying to get in the history books...

I'm trying to hallucinate my entire reality from eternal forms... what does posterity mean to a person like myself?
Ecmandu
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### Re: Negative Zero

Fixed Cross wrote:Such an example presupposes that to divide something by its equal is the same sort of logical operation as to divide it by something different. But I think n/n has no metaphysical bearing on n/p.

The case remains that 0 fits into 1 an infinite amount of times.

Division is a shorthand for subtraction. "6/3" is the number of times you can subtract 3 from 6 before you get to 0. Subtraction is a kind of addition too, just in the other direction (negative is the opposite vector direction to positive). 6/3 can also be expressed as the number of times you need to add 3 to itself (from 0) to get to 6. This is why computers only need "adders" to pull off all mathematical and logical calculations (or more precisely "half-adders", which are just AND/XOR/OR gates in a specific arrangement to channel electrical current in a certain way to make the output look appropriately and usefully different depending on what you input).

To answer 0/0, how many times do you need to subtract 0 from 0, or add 0 to 0 to get to 0? Well you're already there, but you can also do it any number of times, including an infinite number of times, meaning 0/0 is all numbers and no numbers - it's undefinable. The "n" or "p" in your example are incidental, the "/" operation is what's critical, or more precisely the "+" operation implied by"/". In this way, n/n and n/p are metaphysically the same.

"0 fitting into 1" is a kind of pie analogy that has the potential to be misleading - and you could also easily say that 0 never fits into 1. Or are you trying to imply that infinite is the same as never? That would leave you in a bit of a conundrum, if everything (infinity) was nothing (never) to you...

The clear way presents itself to those who understand where maths comes from, which I have described above. n/n when n=0 and and n/0 have no answer just the same way that paradoxes are just badly phrased questions that have no answer until you unpack them and find the internal contradiction that makes them invalid. There are many ways to categorise philosophers: an appropriate one for this situation might be to distinguish those that take on philosophy to solve internal contradictions in order to solve real problems (such as myself) from those who use philosophy as a means towards experiencing awe and mystery (such as Ecmandu and most female philosophers). The latter category gets nowhere with solving anything, instead they only further muddy and complicate things to stoke their imaginations. Whilst I support using your imagination, I do not support speculation for its own sake.

Ecmandu wrote:Silluoette....

Someone once warned me that mathematics is one of the most mud slinging endeavors you can get into... they get vicious.

Negative zero as I'm expounding it, has existential implications. Zero is space, the placeholder, negative zero is all besides the placeholder.

And actually, I'm not trying to get in the history books...

I'm trying to hallucinate my entire reality from eternal forms... what does posterity mean to a person like myself?

Thank you for making the effort to spell my name correctly. I know what you're saying - it's profoundly simple. It's just wrong. I have further explained the role of the "negative" sign/subtraction above - it is more of a vector direction than a NOT, as I already explained and I'm sure you understand even if you won't admit it. Negative 0 is just Positive 0 "but in the other direction" - that is to say they're the same thing.

I already sussed you out, you don't need to explain anything more to me. You want to play with definitions and see what happens. As I said, go ahead, hallucinate. Speculation can be a fun past-time and even lead back to utility in actual reality as long as you bring it back. Philosophy for the sake of philosophy has no end though, so just don't expect me to play along like a fellow child. I'll carry on trying to make reality better using truth with people who want the same instead.

Silhouette
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### Re: Negative Zero

Silhouette wrote:
Fixed Cross wrote:Such an example presupposes that to divide something by its equal is the same sort of logical operation as to divide it by something different. But I think n/n has no metaphysical bearing on n/p.

The case remains that 0 fits into 1 an infinite amount of times.

Division is a shorthand for subtraction. "6/3" is the number of times you can subtract 3 from 6 before you get to 0. Subtraction is a kind of addition too, just in the other direction (negative is the opposite vector direction to positive). 6/3 can also be expressed as the number of times you need to add 3 to itself (from 0) to get to 6. This is why computers only need "adders" to pull off all mathematical and logical calculations (or more precisely "half-adders", which are just AND/XOR/OR gates in a specific arrangement to channel electrical current in a certain way to make the output look appropriately and usefully different depending on what you input).

To answer 0/0, how many times do you need to subtract 0 from 0, or add 0 to 0 to get to 0? Well you're already there, but you can also do it any number of times, including an infinite number of times, meaning 0/0 is all numbers and no numbers - it's undefinable. The "n" or "p" in your example are incidental, the "/" operation is what's critical, or more precisely the "+" operation implied by"/". In this way, n/n and n/p are metaphysically the same.

"0 fitting into 1" is a kind of pie analogy that has the potential to be misleading - and you could also easily say that 0 never fits into 1. Or are you trying to imply that infinite is the same as never? That would leave you in a bit of a conundrum, if everything (infinity) was nothing (never) to you...

The clear way presents itself to those who understand where maths comes from, which I have described above. n/n when n=0 and and n/0 have no answer just the same way that paradoxes are just badly phrased questions that have no answer until you unpack them and find the internal contradiction that makes them invalid. There are many ways to categorise philosophers: an appropriate one for this situation might be to distinguish those that take on philosophy to solve internal contradictions in order to solve real problems (such as myself) from those who use philosophy as a means towards experiencing awe and mystery (such as Ecmandu and most female philosophers). The latter category gets nowhere with solving anything, instead they only further muddy and complicate things to stoke their imaginations. Whilst I support using your imagination, I do not support speculation for its own sake.

Ecmandu wrote:Silluoette....

Someone once warned me that mathematics is one of the most mud slinging endeavors you can get into... they get vicious.

Negative zero as I'm expounding it, has existential implications. Zero is space, the placeholder, negative zero is all besides the placeholder.

And actually, I'm not trying to get in the history books...

I'm trying to hallucinate my entire reality from eternal forms... what does posterity mean to a person like myself?

Thank you for making the effort to spell my name correctly. I know what you're saying - it's profoundly simple. It's just wrong. I have further explained the role of the "negative" sign/subtraction above - it is more of a vector direction than a NOT, as I already explained and I'm sure you understand even if you won't admit it. Negative 0 is just Positive 0 "but in the other direction" - that is to say they're the same thing.

I already sussed you out, you don't need to explain anything more to me. You want to play with definitions and see what happens. As I said, go ahead, hallucinate. Speculation can be a fun past-time and even lead back to utility in actual reality as long as you bring it back. Philosophy for the sake of philosophy has no end though, so just don't expect me to play along like a fellow child. I'll carry on trying to make reality better using truth with people who want the same instead.

And as I stated, it is not just a "not", but an "everything but"
Ecmandu
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### Re: Negative Zero

Let me clarify the convergence of not and negative at zero.

Not zero, implies other numbers, in order to abstract the distinction of zero for any conversation... the not operator solves as every number but.

Opposite of does not imply this except in the case of zero... zero is the lack of all number... which means that every number except zero is being referenced when zero is its opposite, both as other numbers existing as in the first proof, and everything but a placeholder has a place (negative: the opposite of)
Ecmandu
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### Re: Negative Zero

Silhouette wrote:
I/0 is not infinity it is undefinable

The idea that it is infinity presumably comes from any number being divided by smaller and smaller numbers equaling higher and higher numbers that tend to infinity

However consider n/n Something divided by itself always seems to equal I but if n = 0 then do we follow the n/0 = infinity rule or the n/n = I rule

I/0 is supposed to be infinity but that cannot be true because 0 times infinity is still only 0

This raises the interesting mathematical question of what if anything is greater than infinity

Assume for example that I/0 = X then what value would X have ? It would have to be infinity plus
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surreptitious75
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### Re: Negative Zero

Ecmandu wrote:Let me clarify the convergence of not and negative at zero.

Not zero, implies other numbers, in order to abstract the distinction of zero for any conversation... the not operator solves as every number but.

Opposite of does not imply this except in the case of zero... zero is the lack of all number... which means that every number except zero is being referenced when zero is its opposite, both as other numbers existing as in the first proof, and everything but a placeholder has a place (negative: the opposite of)

That's the thing though, negative isn't "opposite of", even at 0. NOT is. Negative is subtraction, which is "addition in the other direction". Does opposite direction mean complete opposite? No. It's still addition, not the opposite to addition. It's only the vector direction that changes, the vector magnitude is the same ergo: not the complete opposite.

What is the addition of 0 in the other direction? Well the magnitude of 0 is the same, so direction (the only thing that distinguishes +0 from -0) doesn't even matter at 0. You can go in any direction from 0 with 0 magnitude and you go nowhere. You remain at 0. -0 = +0 = 0.

!0 however? That's the "opposite of" and it is every number but. The NOT operator is a binary operator, so when applied to 0, it's what you're trying to say -0 is: every number (but excluding 0). As in computing, any number other than 0 is "true" and 0 is "false". True is the opposite of false, and 0 is the opposite of any other number than 0. Maths exists to straighten out the muddying that you can pull off with English, already solving problems like the one you've tried to come up with if you understand it. Yes, you can play around with definitions to see what happens, but what you want -0 to be is already accounted for by !0 so where you're trying to get to has already been gotten to - it serves no purpose.

Silhouette
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### Re: Negative Zero

Silhouette wrote:
Ecmandu wrote:Let me clarify the convergence of not and negative at zero.

Not zero, implies other numbers, in order to abstract the distinction of zero for any conversation... the not operator solves as every number but.

Opposite of does not imply this except in the case of zero... zero is the lack of all number... which means that every number except zero is being referenced when zero is its opposite, both as other numbers existing as in the first proof, and everything but a placeholder has a place (negative: the opposite of)

That's the thing though, negative isn't "opposite of", even at 0. NOT is. Negative is subtraction, which is "addition in the other direction". Does opposite direction mean complete opposite? No. It's still addition, not the opposite to addition. It's only the vector direction that changes, the vector magnitude is the same ergo: not the complete opposite.

What is the addition of 0 in the other direction? Well the magnitude of 0 is the same, so direction (the only thing that distinguishes +0 from-0) doesn't even matter at 0. You can go in any direction from 0 with 0 magnitude and you go nowhere. You remain at 0. -0 = +0 = 0.

!0 however? That's the "opposite of" and it is every number but. The NOT operator is a binary operator, so when applied to 0, it's what you're trying to say -0 is: every number (but excluding 0). As in computing, any number other than 0 is "true" and 0 is "false". True is the opposite of false, and 0 is the opposite of any other number than 0. Maths exists to straighten out the muddying that you can pull off with English, already solving problems like the one you've tried to come up with if you understand it. Yes, you can play around with definitions to see what happens, but what you want -0 to be is already accounted for by !0 so where you're trying to get to has already been gotten to - it serves no purpose.

Oh, c'mon....

Negative 2 is not the subtraction of 2.

2-2 equals zero.

The distance as an opposite is 4!!!

It's not subtraction, it's opposite of
Ecmandu
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### Re: Negative Zero

Ecmandu wrote:Oh, c'mon....

Negative 2 is not the subtraction of 2.

Oh, it really is

That you don't know this explains a lot about what you're trying to do here.

2 is the addition of 2 from 0 = "0+2". 0 is that same 2 but once you "-2": the subtraction of 2 from 2, or the addition of 2 but in the opposite direction back from 2.... to 0. It's all very very simple.

What is "the distance as an opposite is 4" supposed to mean? 2-(-2) is 4, sure. How are you trying to misread me here?

Silhouette
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### Re: Negative Zero

Silhouette wrote:
Ecmandu wrote:Oh, c'mon....

Negative 2 is not the subtraction of 2.

Oh, it really is

That you don't know this explains a lot about what you're trying to do here.

2 is the addition of 2 from 0 = "0+2". 0 is that same 2 but once you "-2": the subtraction of 2 from 2, or the addition of 2 but in the opposite direction back from 2.... to 0. It's all very very simple.

What is "the distance as an opposite is 4" supposed to mean? 2-(-2) is 4, sure. How are you trying to misread me here?

I was a step ahead of you... 2 - (-2) is a double subtraction, which inverts what I said about subtraction itself. I'll just forget that you ev n bothered to say subtraction is addition.
Ecmandu
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### Re: Negative Zero

Ecmandu wrote:I was a step ahead of you... 2 - (-2) is a double subtraction, which inverts what I said about subtraction itself. I'll just forget that you ev n bothered to say subtraction is addition.

Opposite direction to the opposite direction is the same direction.... so?

Like I said, don't look to me for confirmation that subtraction is addition, just learn how computers work. Subtraction is addition... but in the opposite direction (same magnitude). Does that mean subtraction = addition?

Seriously, how are you misunderstanding me, maths and computers so badly? One step ahead? If ahead means in the opposite direction, sure.

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