Talk:Negative number

This situation cannot be understood as repeated addition, and the analogy to debts doesn't help either. The ultimate reason for this rule is that we want the distributive law to work:

(3 + (-3)) · (-4) = 3 · (-4) + (-3) · (-4).

The left hand side of this equation equals 0 · (-4) = 0, while the right hand side equals -12 + (-3) · (-4); for the two to be equal, we need (-3) · (-4) = 12.

I didn't understand the above, so I just cut it and pasted it. I hope the sections on arithmetic with negative numbers are correct, as well as clear, now. Someone really ought to check me, because in my haste I could easily make a non-negative number of errors :-) --Ed Poor 20:58 Dec 5, 2002 (UTC)

Makes sense to me. Follow the brackets carefully, Ed. negative * negative always did make sense to me as a repeated addition when I was a kid. 2 * -3 means "two lots of -3", -6, and since this can be also written as -3 * 2, it seemed logical to interpret this as "-3 lots of 2". hm. years since I thought about this stuff... -- Tarquin 10:26 Dec 6, 2002 (UTC)

Removing:

Multiplication of a number by -1 changes its sign. This is called negation, and may be expressed by placing a minus sign in front of a number or a quantity in brackets:

-1 × 5 = -5

-1 × -8 = -(-8) = 8

-1 × (3 + 4) = -(3 + 4) = -7

In fact, negation is equivalent to multiplying a number by -1:

-5 = -1 × 5

This equivalence can be used to simplify multiplication involving negative terms:

-6 × 3 = (-1 × 6) × 3 = -1 × (6 × 3) = -1 × 18 = -18 (if you have a debt of $6, and then your debt is tripled, you end up with a debt of $18.)

Multiplication of two negative numbers yields a positive result:

-3 × -4 = (-1 × 3) × (-1 × 4) = (-1 × -1) × (3 × 4) = 1 × 12 = 12, or more simply,

-3 × -4 = -1 × (3 × -4) = -(-12) = 12

since negation was something I remember had to be proven in analysis, I'm not entirely sure how correct it is to just blankly state it. Restoring Axel's version for now, until he's back to maybe take the best of both & merge. -- Tarquin 11:15 Dec 6, 2002 (UTC)

Doesn't this just follow from 0*x = (1 + (-1))*x = x + -1*x = 0, so that -1*x is guaranteed to be the additive inverse (i.e., negation) of x, denoted by -x? Chas zzz brown 11:32 Dec 6, 2002 (UTC)

That's nothing. I'm waiting for the AE/BE argument to start about whether it should be math or maths... Maybe we should just use mathematics all the time to be safe. ;) --Dante Alighieri 11:18 Dec 6, 2002 (UTC)

Yup, you're right, Chaz. It's hard to determine how axiomatic to be in covering what the lay readers takes to be a very basic topic. -- Tarquin

Hold on. I really don't think it makes much sense to merge Positive number and Nonnegative into Negative number. They're not the same thing, after all. I don't expect to read about positive numbers in an article called "negative number". Evercat 13:03 21 May 2003 (UTC)

There is no doubt they are not the same thing. How about the title negative and positive number? -- Taku 13:08 21 May 2003 (UTC)

That would be better. Perhaps Negative and positive numbers is grammatically better. Still, I rather prefer seperate articles for them, all linking to one another... Evercat 13:11 21 May 2003 (UTC)

Since wikipedia is an encyclopedia, I think it makes more sense one article talks about negativity of number. Currently the article is nothing more than a bunch of definitions and properties, but we certainly want to discuss when the concept of negative is introduced, notations and other stuff. I don't think positive number article can grow more than a mere dictionary entry. (I don't mean to impose my will but just trying to justify why I did. We can discuss this.)

-- Taku 13:17 21 May 2003 (UTC)

noo!! the example at the bottom uses two-complement!! if the leftmost bit is used to express the sign (wich it seldom does in processors!) it cannot express -128 but only -127. there is also two zero's, -0 and 0, wich makes some operations quiet odd: -3+4 = 0, wich is wrong..? :P

I thought the example I put is quite typical. If I remember correctly, char of C can express -128 to 127 because there are 255 distinct numbers. There should be only one zero. -- Taku 19:15 21 May 2003 (UTC)

That's in two's complement. In one's complement, a negative number is represented as the complement of the value. Thus, the top bit is "1" if the value is negative. A weird thing about one's complement is that there are two representations for zero (all zeros and all ones). One's complement is much less common today, but it's still important historically -- Dwheeler 19:30 21 May 2003 (UTC)

This seems quite interesting. If you can, don't hesitate to add this scheme (called one's complement?). The article certainly doesn't have to be limited to one mechanism. -- Taku 22:00 21 May 2003 (UTC)

A more detailed discussion is already in Integral data type, and this article ("Negative and positive numbers") links to it.

Negative and positive numbers... hm... so that's like numbers except 0.

Zero, the square root of zero, the cube root of zero, zero squared. ;) --Dante Alighieri 19:25 21 May 2003 (UTC)

Dante, you little sound sarcastic, but really I didn't notice numbers except 0, but then do you have any idea how to name this article? Topics like representation of negative and positive numbers in computers look weird if they are located in negative number article. -- Taku 21:51 21 May 2003 (UTC)

Why not put all this information on number? -- Minesweeper 22:01 21 May 2003 (UTC)

Good point. Why not? Any objection? -- Taku 22:02 21 May 2003 (UTC)

All this detail about how to add and subtract negative and positive numbers would be a burden in "Number". However, cross-links sure make sense. Having this as a separate article makes it easier to reference specifically the issue of + vs. -.

Then what about negativity or even the concept of negative number. If possible, we certainly want to add about the history of negative numbers. -- Taku 22:27 21 May 2003 (UTC)

Yes. It sounds like there's many good reasons to leave this as a separate page. -- Dwheeler 22:30 21 May 2003 (UTC)

I would like to rename this to negativity because I knew negative and positive numbers sound like any number but zero, which is not the intent of this article. Any objection? -- Taku 22:57 21 May 2003 (UTC)

To me negative number would make more sense than negativity, for one thing because the latter does not make it perfectly clear that mathematics is the subject. Negativity (mathematics) seems overly complicated. Michael Hardy 00:08 22 May 2003 (UTC)

But what about "I don't expect to read about positive numbers in an article called "negative number" by User:Evercat. He has a point. It seems little weird the article negative number has a lot of mention about positive numbers. But the trouble we invented a concept positive number after invension of negative numbers. Without the concept of negative number, we don't have positive numbers. Then a compromise, how about negative and non-negative numbers? Sounds strange? -- Taku 02:24 22 May 2003 (UTC)

I think it's fine where it is. The discussion of where zero falls is natural for an article called "negative and positive numbers". Evercat 14:24 22 May 2003 (UTC)

They're called signed numbers! -- Toby Bartels 04:14 6 Jun 2003 (UTC)

I revert new move since there seems no agreement with it yet. -- Taku 04:21 6 Jun 2003 (UTC)

I was bold since (unlike some page moves) it could be undone if somebody didn't like it (as you don't). But I'd like to hear your opinions of disagreement too! -- Toby Bartels 04:42 6 Jun 2003 (UTC)

First of all, I have never heard of signed numbers. I mean is it really a popularly accepted term? Do you have evidence? If you do, I have no trouble to restore your contribution myself. -- Taku 04:48 6 Jun 2003 (UTC)

I hear it often enough -- though this is hearsay. There's some evidence in the article itself, where people other than me used the term. But I should provide some documentary evidence of use outside of computer science too, so I'll go look some up. -- Toby Bartels 09:58 11 Jun 2003 (UTC)

I really don't see why this page exists at all. Initially it was about negative numbers. What was wrong with that?? Then it became negative and positive numbers, until someone pointed out that it was a bit silly that it excluded zero (ohh year that was me). Now it's about er .. what ? er... numbers. Content should be moved to either number or integer where negative numbers can be discussed in context. The stuff about binary representation of negative numbers is already well covered in Computer numbering formats. The use of links where appropriate should suffice. Mintguy 16:39 6 Jun 2003 (UTC)

You seem to be correct about the computer representation (although Computer numbering formats needs to be broken up). Signed numbers are a separate concept from simply integers, since one may consider signed or unsigned numbers of other sorts (like rational, real, cardinal, etc). This article could talk about the common issues, while Integer would deal with the specific properties of Z (like its special position among rings). -- Toby Bartels 09:58 11 Jun 2003 (UTC)

Agreed. Could we have a simple page title back, ie negative number? -- Tarquin 18:56 6 Jun 2003 (UTC)

While I like Signed number, I also see no reason why Negative number and Positive number can't also exist separately. And maybe when all the material specific to those articles, to Integer, and to Computer numbering formats is taken out, there'll be very little left of Signed number (or whatever you want to call it), in which case it can be folded into Number. -- Toby Bartels 09:58 11 Jun 2003 (UTC)

Though strage title, I think having a separate article about the concept of negative numbers in math or its representation does make sense. I don't think negative and positive is part of number. Breaking up the article to two articles doesn't make sense. Any article in wikipedia is an encyclopediac article, which means we want to discuss not just what it is, but also more about history, significance in society and so on. Unfortunately there are a lot of overlaps between Computer numbering formats and other wikipedia articles. Rather than moving stuff here to it, it should be more reasonable to move stuff from there to here as we break up the article. -- Taku 21:30 11 Jun 2003 (UTC)

Computer numbering formats. Actually It is a really good written article but the trouble is that the article is rather isolated from the rest of well-cultivated wikipedia articles. The stuff about binary represention is vital because the article should not be limited to that in math but that in general cases. Besides, in the future we might want to add portions for example history of concept of negative and positive. Actually I don't have much trouble to rename this to simple negative number but then what about positive number then? Are people suggesting split it off into two articles? Honestly I really don't like a current ugly title but I don't know a better one. Actually it is rather silly to discuss a lot about naming because unlike dictionaries, in encyclopedia articles, the article tends to be more general, thus, sometime the title also tends to be complex. For example, political status of Taiwan or something (I don't remember the current name). -- Taku 22:04 6 Jun 2003 (UTC)

I don't think the title of this article is as important as its contents: the discussion of 1-complement, 2-complement etc. does not belong here, only a link. After all, that is a discussion of numerals for negative numbers in the binary system, not of negative numbers themselves. What we desparately need however is a history section. AxelBoldt 15:04, 29 Sep 2003 (UTC)