Negative Zero

Yes I think you’re right.

+1 is the opposite of -1, but not-1 means any number that is not 1.

Infinity is undefinable :wink:

A negative beaver is a tallywacker. They live in the forest and visit the bush during mating season. :slight_smile:

That’s prescient! :wink:

Neither zero nor infinity exist.

If you have zero apples, you have a non-existence of apples. If you have infinite apples, you have a non-existence of apples.

The only thing that can be ubiquitous is nothingness and the only thing there can be infinite amount of is nothing.

If there were infinite apples, there would be nothing that’s not-apple, and therefore there would be no context in which the apples could manifest.

I’m going to reply to this by simply stating: the issue at hand is zero, and strange properties of zero relative to non zero numbers.

To use non zero numbers as analogies is to miss the argument completely.

Actually that charge silloutte is is brining against me is not “sophistry” as claimed, but rather “equivocation”.

I stated outright that these are modalities of math and that mine is grammatically correct … to silhouette, this is putting words on people’s mouths, to which I replied, these are different modalities.

I perfectly well stipulate that I know nothing of reality. I’m not even convinced there is one. We could be a brain in a vat, an experiment in an alien grad student’s AI lab, or a program running in God’s own Turing machine. I try to clarify mathematical issues when they come up. But I certainly have no idea of what’s “out there.” Personally I don’t think the standard real numbers are literally how reality works. To me, the real numbers are a wonderfully interesting mathematical abstraction that probably have no relation at all to the world. Or maybe they do. It’s fun to talk about.

Absolutely. I feel like I spend my life trying to explain this to people online. Then other people try to explain it to me, as if they think I’m arguing the opposite.

Ah sorry part with you here. When we try to formalize our vague intuitive notions of infinitesimals, we find that there is not a smallest positive real number in ANY conceivable model of the real numbers, in particular the hyperreals, which are everyone’s go-to example of a system of numbers with infinitesimals.

So if you are making a philosophical point, you still can’t violate known math. If I’m understanding you correctly.

Ok.

Ah I see where you’re going with this. No, there is no smallest number or infinitesimal just to the right of zero. Because if you say there is, and you call it x, then I’ll just point out that 0 < x/2 < x and x was not the smallest after all.

That’s math, brotha.

But zero is nothing… absence of things. How can nothing have properties?

Sophistry implies mal-intent, right?

What you’re on about reminds me of this video:

Start “just to the left of” 5:00 :wink:

[youtube]https://www.youtube.com/watch?v=emlcwyvnsg0[/youtube]

You’re perfectly correct in math, but in what we colloquially regard as reality there are limits to numbers.

Check out this video. Start at 10:00

[youtube]https://www.youtube.com/watch?v=WabHm1QWVCA[/youtube]

Here’s a longer lecture if you’re really interested:

[youtube]https://www.youtube.com/watch?v=p9xX-Jpsr_E[/youtube]

You are conflating the mathematical with the physical
Zero is a number and numbers are not actual things
The properties in question are purely mathematical

Some video some guy made is not proof of anything. Even if I spent 30 minutes of my life watching it, if I disagreed with anything he said I’d just be arguing with some guy who made a video. What is the point of that?

If you can state an argument relevant to my post we can have a discussion. You and I, not me and some guy on the Internet with an opinion. I can’t argue with every Youtube video that’s out there. I’d have to make my way through the flat earthers and the moon landing deniers long before I got to the infinity opinionators.


That second video you posted looks very interesting so I will watch it later today

Some guy?

I am a professor of mathematics at UNSW Sydney. I was educated at Adam Scott High School in Peterboro Ontario, Richmond Hill High School in Richmond Hill Ontario, University of Toronto (BSC 1979) and Yale University (PhD 1984). I taught at Stanford University (1984-1986) and the University of Toronto (1986-1989) before coming to UNSW (University of New South Wales), Sydney, in 1990. web.maths.unsw.edu.au/~norman/

My PhD thesis was Quantization and Harmonic Analysis on Nilpotent Lie Groups. I have worked in representation theory, harmonic analysis, combinatorics, and geometry. I have developed finite hypergroups and duality, Pell’s equation and Diophantine equations, and introduced Rational Trigonometry and chromogeometry (download my book here!) I have reformulated hyperbolic geometry to make it more algebraic, general and beautiful. I have a YouTube channel: njwildberger with 600+ math videos. researchgate.net/profile/Norman_Wildberger

It would be like calling Stephen Hawking “some guy”.

I told you FWD to 10:00. It’s like 1 min and if you’re interested, then listen to the other. If not, then don’t.

Stay ignorant. I don’t care.

It’s as if you said “If you do not feed me the information I want in the form I want it, I’m going to stay uninformed! So there!” ← Not scary.

I did. The universe presents a limitation on math. Watch the accomplished and passionate mathematician say it again on the video along with his reasoning.

You went so far into left field that you’re in the parking lot.

Why would you have to watch flat-earthers and moon landing deniers before watching 1 min of the video I posted?

But even in math it’s nothing and for a long time, zero wasn’t even regarded in math. livescience.com/27853-who-i … -zero.html

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

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.

This thread is a lot of ado about nothing lol

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 :wink:

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.

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!

I totally don’t understand that.

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.

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

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.

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.

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.

I’m not tracking your line of thought. You talked about floating point numbers. That’s not historical, that’s just a category error, responding to a question about apples with an answer about armadillos.

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

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?

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?

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.

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

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)

I can see that, but that’s infinity, no? “Every number” is an unbounded concept.

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.

That’s infinity.