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### Re: Negative Zero

Posted: Wed Aug 01, 2018 10:52 am
There were other things that were once unknown in maths such as irrational numbers and negative integers and complex numbers
But once they were discovered they were seen to be incredibly useful so the fact that zero was also unknown means nothing at all

You need zero because apart from anything else without it you would have no base ten
It is also unique as it is the only non negative / non positive integer on the number line

### Re: Negative Zero

Posted: Wed Aug 01, 2018 8:08 pm
surreptitious75 wrote:the fact that zero was also unknown means nothing at all

Idk, it wasn't that zero was unknown so much as I think it was rejected because why do I need to write down that I have no cows? People didn't need to keep track of nothing. Maybe zero only became relevant when negative cows came about: I owe 2 cows to my neighbor and one day hope for zero cows instead of -2.

Every number has an opposite: n and -n. That is true with the exception of zero, which has no polar mate. But the opposite of nothing is the ubiquitous or infinity. So zero does have a mate even though neither exist.

### Re: Negative Zero

Posted: Wed Aug 01, 2018 10:59 pm
wtf wrote:Ok now I feel terrible. You shouldn't have been so nice to me!!

Not at all, it's possible from what I can tell from your words that you might actually have something to teach me. That will involve pointing out legitimate flaws in my argument, so feel no guilt for it. To be honest, I was tired of the repetitious illegitimate criticism that I was receiving. It frustrates me so when it's so clear to me that the respondent is so very misguided - and by contrast, I seem to be recognising you as somebody who actually has knowledge about that which you're talking.

Wetness aside, by all means let's challenge this assumption and see if we can't fall out as in all proper internet arguments

Some clarification though: my maths background actually extends much further than my computing one, though I won't deny that my computing has had an influence on it and given me some insight into maths that I did not have before. Actually though, I am mostly basing my arguments loosely on a history of mathematics: starting with natural numbers, through subsequent discoveries of other categories that did not accord with the previous ones. It all started off with addition forwards and backwards (subtraction) - although it wasn't necessarily the case that it was thought of in this way, "backwards addition" is more of a reductive perspective as I've already said. More than likely it was just thought of as "this much more" vs "this much less": backwards addition is just a way to think of it that was inspired by my education in computing. With integers, multiplication and division ought to be fairly straight-forwardly a shorthand for multiple additions/subtractions. Of course this runs into problems are you start branching out past natural numbers through integers and fractions to irrationals and beyond (what I am referring to as "anomalies" compared to what preceded them) - I'm just explaining how we got there. I assume that your post was to catch me out by shifting the foundation from the beginning of mathematics to something more contemporary where things are much more complicated. Perhaps you recognised my approach and wanted to change the context to something more modern - and why not? I admit conceptions have moved on from my explanation of how maths started. My contribution to this thread, though, was in the certainty that at no point has it ever been appropriate to equivocate by equating "NOT" with "negative" - nor will it ever be. That was the whole reason I brought computing into it: what was being described was the NOT function, as in computing, only it was erroneously being called the "negative" operator.

### Re: Negative Zero

Posted: Fri Aug 03, 2018 2:50 am
Silhouette wrote:Not at all, it's possible from what I can tell from your words that you might actually have something to teach me. That will involve pointing out legitimate flaws in my argument, so feel no guilt for it. To be honest, I was tired of the repetitious illegitimate criticism that I was receiving. It frustrates me so when it's so clear to me that the respondent is so very misguided - and by contrast, I seem to be recognising you as somebody who actually has knowledge about that which you're talking.

Thaks again. But remember it's an online forum. What forums sometimes lack in sanity and/or knowledge they make up in free speech and alternate points of view. So rather than be frustrated, we should enjoy online forums for what they are, which is NOT the proceedings of the Royal Society!

Silhouette wrote:Wetness aside

I totally don't understand that.

Silhouette wrote:by all means let's challenge this assumption and see if we can't fall out as in all proper internet arguments

Looking ahead, I did not see a clear thesis or question articulated. I think we agree that multiplication was originally repeated addition, both at the level of mathematical development and individual student understanding. You seem to be emphasizing that but I perfectly well stipulate it. I could not get a grip on what point you are making or what my reponse should be.

Silhouette wrote:Some clarification though: my maths background actually extends much further than my computing one, though I won't deny that my computing has had an influence on it and given me some insight into maths that I did not have before. Actually though, I am mostly basing my arguments loosely on a history of mathematics: starting with natural numbers, through subsequent discoveries of other categories that did not accord with the previous ones.

Ok. Also paragraphs? That would help. I know, I'm a born critic. Still.

Silhouette wrote:It all started off with addition forwards and backwards (subtraction) - although it wasn't necessarily the case that it was thought of in this way, "backwards addition" is more of a reductive perspective as I've already said. More than likely it was just thought of as "this much more" vs "this much less": backwards addition is just a way to think of it that was inspired by my education in computing. With integers, multiplication and division ought to be fairly straight-forwardly a shorthand for multiple additions/subtractions. Of course this runs into problems are you start branching out past natural numbers through integers and fractions to irrationals and beyond (what I am referring to as "anomalies" compared to what preceded them) - I'm just explaining how we got there.

Ok. You and I are in perfect agreement that in the development of humanity, and mirrored in the development of the individual human, numeracy proceeds from abstracting numbers of things to numbers, and then taking successors and adding numbers, and then multiplication is repeated addition. Nobody's debating that. I hope that's clear.

Silhouette wrote:I assume that your post was to catch me out

No I didn't post to "catch you out." You answered a question about the mathematical real numbers by giving a detailed exposition of floating point arithmetic in computers. I thought that was such a large category error that I called it out.

Calling out an error is not "catching you out." Catching you out is trying to trick you. I'm not trying to trick you. I'm trying to explain to you that the mathematical real numbers are as far removed from IEEE-754 floating point as fine wine is to grape juice. Bad grape juice.

Fun fact: Determining whether a floating point number is zero is not computable. Now how lame is that? You can't even recognize zero.

Silhouette wrote:by shifting the foundation from the beginning of mathematics to something more contemporary where things are much more complicated.

Well it's not 1400 anymore. If you want to talk about the mathematical real numbers, the default is that we are talking about them as they are understood by contemporary mathematicians. If you want to talk history, say that.

But I'm confused. You answered a question about the real numbers by saying something about floating point numbers, a completely different topic. I don't understand why you did that. I still don't.

And now I don't understand why you are saying your approach is historical. I'm a little lost in your argument.

Silhouette wrote:Perhaps you recognised my approach and wanted to change the context to something more modern - and why not?

But sure, historically multiplication was repeated addition. Ok. If that's your point, I agree with it.

Silhouette wrote:I admit conceptions have moved on from my explanation of how maths started.

I don't feel that you have addressed my concern that you think IEEE-754 describes the mathematical real numbers. You said that you've studied math but you didn't address the point. Why did you talk about floating point? That doesn't tell us anything about the real numbers. And it's not historical.

See my dilemma? Am I at least making clear why I'm confused at what you wrote?

Silhouette wrote:My contribution to this thread, though, was in the certainty that at no point has it ever been appropriate to equivocate by equating "NOT" with "negative" - nor will it ever be.

I take no position on other aspects of this thread, nor am I responsible for any words other than my own. Why u tellin' me dis?

Silhouette wrote:That was the whole reason I brought computing into it: what was being described was the NOT function, as in computing, only it was erroneously being called the "negative" operator.

Ah ... well ... hmm ........ let me think about that. No. Not buying it. I asked you about the real numbers and you told me about floating point. So this wasn't anything to do with that.

Well ok I hope you found some of this entertaining. We didn't even get to talk about the real numbers yet.

### Re: Negative Zero

Posted: Sat Aug 18, 2018 3:33 pm
But zero is nothing ... absence of things How can nothing have properties

Zero is not nothing.
zero is the center of the system of axes.

Just like 1 isn't "a" or "an".

A number is a place and an element in a system. The introduction of the zero completed the system that existed before.

Numbers are systemic, they don't mean anything outside of a system. For that reason, any given number implies the whole system.

Which is why we work with the matrix

123456789
246813579
369369369

etc

### Re: Negative Zero

Posted: Sat Aug 18, 2018 8:09 pm
Fixed Cross wrote:
But zero is nothing ... absence of things How can nothing have properties

Zero is not nothing.
zero is the center of the system of axes.

Just like 1 isn't "a" or "an".

A number is a place and an element in a system. The introduction of the zero completed the system that existed before.

Numbers are systemic, they don't mean anything outside of a system. For that reason, any given number implies the whole system.

Which is why we work with the matrix

123456789
246813579
369369369

etc

Are you sure there isn't a distinction between writing and math? The origin of the axes and placeholder in numbers is a matter of graphics and not the same as the actual concept of zero. I can type a "0" and it exists, but the concept I'm conveying is "absence of". It's like the word "nothing" is something, but represents the concept of nothing.

1000 is shorthand for one thousand, no hundreds, no tens, no ones. What does "no ones" look like? Nothing. It's the absence of everything in its universe.

(0,0) is a point that is a "nothing amount" in either direction.

0^0 is a little harder to make sense of lol

### Re: Negative Zero

Posted: Sat Aug 18, 2018 8:19 pm
My point is that -1 is the opposite of 1 ... just like cold is the opposite of hot, with an infinite number of things between them.

When dealing with zero, the opposite of zero is every number.

NOT does not mean the opposite of, it means the absence of. For example: since every number is built from one, NOT 1 would = no numbers, which is zero, and NOT zero would be all numbers.

Likewise, the reciprocal of zero, is also every number (the taking away of it)

### Re: Negative Zero

Posted: Sun Aug 19, 2018 5:42 pm
Ecmandu wrote:My point is that -1 is the opposite of 1 ... just like cold is the opposite of hot, with an infinite number of things between them.

When dealing with zero, the opposite of zero is every number.

I can see that, but that's infinity, no? "Every number" is an unbounded concept.

NOT does not mean the opposite of, it means the absence of. For example: since every number is built from one, NOT 1 would = no numbers, which is zero, and NOT zero would be all numbers.

Looks to me that "not" can be used in two different contexts. "Off" = "not on" and they're opposites by virtue of duality. Usage of "not" should come with qualifications.

Likewise, the reciprocal of zero, is also every number (the taking away of it)

That's infinity.