Talk:Negative number

Through 2003

Added rules for division (in quite simplistic terms, since this is the same as multiplication -- same sign -> positive result, different signs -> negative result).

I get the point that the article is meant to be understood easily, but can't we just refer to things by their names? Using words like "dividend" and "divisor" (for division) or "factors" (for multiplication) makes much more sense to me than exhaustively mentioning "if you add a positive number to a negative number"... you get the idea. ;) --doshell

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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.

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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)

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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

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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

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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)

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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)

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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)

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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)

Classification of 0

Mathematically, 0 is neither positive nor negative. However, in naive English it is common to use the word "positive" to include 0. Any comments about this?? 66.245.1.229 19:30, 6 Nov 2004 (UTC)

It may or may not be naive, but it would certainly be confusing and misleading to call zero a positive number. If I say that "I have visited Paris a positive number of times" I would mean I have done it at least once. --Henrygb 22:32, 17 Nov 2004 (UTC)

People don't use their languages correctly many times. But I think it is unnecessary to mention such misuses in too much detail. -- Taku 01:38, Nov 18, 2004 (UTC)

Did you mean to say "naive English" or was that supposed to be "native English?" As a native English speaker, I've never heard anyone refer to zero as a positive number, except when discussing the mathematical classification, in which case they were simply wrong. -- Foof 03:04, 6 February 2006 (UTC)

It's increasingly common in mathematics to distinguish, in general, between positive and strictlyt positive objects, abolishing the slightly awkward term non-negative (for example, a complex number is usually neither negative nor positive nor 0. In order of increasing generality, the possibilities are:

• a linear order with 0. The usual terminology is positive, negative, zero, as in the article.
• a partial order with 0. There are now elements that are incomparable to 0, and being non-negative no longer means being positive or 0. That's why for complex numbers, the longer term "nonnegative real number" is sometimes used.
• several partial preorders with 0. That's the tricky one. It's not at all uncommon these days, and there is usually no good way to say "an element that is nonnegative in every individual preorder".

To illustrate (and to give me some practice with tables, but don't tell anyone I wasn't perfect before), consider the space R² (that's just maths-speak for tuples of real numbers):

Element	"old" terminology	"new" terminology	"new expanded" terminology
(1,1)	positive	positive	strictly positive
(1,0)	?	positive	varies
(0,0)	zero	zero or positive or negative	zero or positive or negative
(0,-1)	?	negative	varies
(-1,-1)	negative	negative	"strictly negative"
(1,-1)	?	?

Now, it turns out that in such general cases, it usually turns out that there are many useful theorems about the "new" positive elements; sometimes there are useful theorems about the "new expanded" strictly positive elements, including or excluding the (1,0) case depending on which object you deal with. The set of "old positive" elements is usually far less interesting, and when it is interesting, there is virtually always a set of preorders such that it becomes the "strictly positive" set, and the positive set will be interesting then, too!

In short, many mathematicians, including myself, think it is an unfair accident of history that "positive" excluded the zero case. It is also questionable etymologically (it is quite possible to put zero apples on a table. It's much harder with -1 apple, particularly if there aren't any on it to begin with).

I definitely think that this should be discussed in an article linked to from positive. It is also worth mentioning that 0 is "positif", in French, and that this practice has spread through adoption of French terminology.

Finally, since this is something that people argue about a lot until they finally go find a mathematician who is subsequently annoyed at being asked again, it's a convention. Mathematicians tend not to feel strongly about which convention you use, though they do feel strongly about wasting a lot of time because you used a nonstandard convention without telling them. Still, it is a convention, and if you prefer another one, just state so clearly and move on.

RandomP 00:30, 1 May 2006 (UTC)

As I see here some discussion has already been held about the topic of positivity of zero. One ting hasn't been mentioned yet, namely the fact that the current definition is inconsistent: "A positive number is a real number that is greater than zero, such as 2. Zero itself is neither positive nor negative." Since a is greater than b means (by defenition of order, whether it's total or partial) that $b\leq a$, the first part of the definition tells us that, since $0\leq 0$, 0 is a positive number, a statement that is contradicted in the next sentence. If wikipedia indeed is in favor of not calling 0 a positive number (I myself would say it is), this could be corrected by changing 'greater than zero' in 'strictly greater than zero'. What about it? HSNie (talk) 18:56, 29 May 2009 (UTC)

No inconsistency. You got the definition of greater wrong. What you put in was greater than or equal. Dmcq (talk) 23:03, 29 May 2009 (UTC)

I'm pretty sure I'm not mistaken in that. One of the first pages of my book on order/lattice theory even mentions it as a common misconception among non-mathematicians to think that greater than means > instead of $\geq$. HSNie 23:22, 30 May 2009 (UTC) —Preceding unsigned comment added by HSNie (talk • contribs)

That is simply not true. If you do find a book saying something like that please give a reference to it. In mathematics greater than corresponds to the sign > and excludes the case of them being equal, greater than or equal corresponds to ≥. See Inequality Dmcq (talk) 01:43, 31 May 2009 (UTC)

bad jokes and other non...negatives

no comment on the following :

• "Division is similar to multiplication"
• "If both have different signs"

some comments on the folllowing :

• nonnegative can be defined as desired, but "non negative" has (imho) the meaning of "not negative" and is thus invariably defined once "negative" is defined. For example, an imaginary number is not negative.
• in the context of "nonnegative matrix" I think one should include not only links but also comments to what is commonly called a positive matrix (for which the associated quadratic form takes ony nonnegative values)

I don't want to impose my ideas and thus don't make changes since this might be controversal, and I risk to be too axiomatic: I would call nonnegative all elements that are not less than zero (in any group equipped with a partial order), so this is not always the same than "positive or zero"; and suggest to specify "nonnegative reals" or "nonnegative integer" etc. in order to get the "usual" (particular) meaning.

But if someone feels an inspiration, I strongly suggest to make the adequate changes. — MFH: Talk 13:16, 28 September 2005 (UTC)

First usage of negative numbers

From the current article:

"Negative numbers were not well-understood until modern times. As recently as the 18th century, the Swiss mathematician Leonhard Euler believed that negative numbers were greater than infinity..."

This seems unfairly closed-minded. The convention that −1 < 1 is natural if you want an ordered group, but some uses of negative numbers demand a different ordering: see negative temperature. Melchoir 01:08, 11 February 2006 (UTC)

Diophantus

Diophantus's rejecting 20x+4=0 as a meaningful equation is cited as an evidence of knowledge of negative numbers in Greece. This is absurd, since it is a clear evidence to the contrary. It's like saying that somebody rejecting square root of negative numbers is an evidence that he knows imaginary numbers. deeptrivia (talk) 03:18, 17 February 2006 (UTC)

off the current topic slightly. can anyone prove the existance of negative numbers? i dnt mean prove as in negative temperatures i mean prove lik u would prove the quadratic equation by using completing the square or prove the sum to infinity for a geometric series.

The short answer is yes, but the longer answer is long indeed. After all, what do you mean by "existence"? One construction of negative numbers is given by the "Formal construction of negative and non-negative integers" section of this article. If you want a thoughtful explanation of what it all means, I think you'll get an excellent response if you ask on Wikipedia:Reference desk/Mathematics. Melchoir 17:50, 9 June 2006 (UTC)

In fact, Diophantus knew about negative numbers (or better: quantities) and calculated with them, he just did not accept them as a (final) result, as he found a negative result as absurd or useless. This is very well shown in: "Negative Größen bei Diophant?" (2007) written by Klaus Barner. Unfortunately, it is not written in English but in German, which might be the reason for it seemingly not being very popular. Isabella G. Bashmakova is said to have shown it (i.e. that Diophantus knew negative numbers), too (though I haven't read her book, yet). It would be great, if anybody speaking english better than me amended the article in this respect. —Preceding unsigned comment added by 91.36.93.115 (talk) 12:51, 23 August 2010 (UTC)

Minus numbers?

Terminology is important. It's time for a rant.

If I Google "negative number" I get 2,470,000 hits, and all of them are coherently talking about negative numbers. If I Google "minus number" I get 53,100 hits. Even of those, I grow suspicious: out of the top 10 hits, only 4 are actually talking about negative numbers; another 4 are using "minus" as a verb, and the other 2 are incomprehensible.

So I Google "negative numbers" with an s, and this time I get 3,060,000 hits, and all of them are coherently talking about negative numbers. But "minus numbers" gets 17,000 hits, and even then the very top item is an incomprehensible PDF technical sheet in all caps; below that is a subject-line of some student asking "dr. math", and further below we find such gems as "NBA Plus Minus numbers for the last 30 days!". On the next page there are three more "plus/minus" phrases.

I conclude that virtually no one says "minus numbers", including the British; that even in the rarity when they do use the phrase it's even odds on what they mean; and of that tiny minority who actually use it to mean "numbers less than zero", they're either double-talking pedagogues or just confused.

If we search Wikipedia itself, it gets even better: all of the bolded phrases at the top are used throughout the project, even "non-positive numbers". "Minus numbers" turns up nothing.

Even if we assume that all the searches are lying to us: I've read mathematics books at all levels; I've read research articles written from all over the world; I've even read the literature for elementary school teachers. They all say "negative number", and more importantly, none of them says "minus number". If anyone has a reliable source that says "minus number" for a number less than zero or naught, please cite it and educate me. Until then, there is no need to encourage or even acknowledge confusing and truly obscure terminology. Melchoir 05:48, 23 March 2006 (UTC)

The usage is not all that obscure. The first page of a Google Book search turns up several usages, some of which seem like they could be called a reliable source:

• [1] Practical Statistics Simply Explained by Russell A Langley - Mathematics - 1971 - 399 pages. Page 61 - "Remember that a minus number multiplied by another minus number gives"
• [2] Basic Ac Circuits by Clayton Rawlins, John Clayton Rawlins - Technology - 2000 - 541 pages. Page 400 - "There is no real number which when squared results in a minus number."
• [3] Statistics Explained: A Guide for Social Science Students by Perry R Hinton - Mathematics - 1995 - 256 pages. Page 31 - "if you calculate a z score and it turns out to be a minus number, all this means is that the score is less than the mean."
• [4] Conduct of Monetary Policy (pursuant to the Full Employment and Balanced Growth Act of 1978,... by Finance, and Urban Affairs United States. Congress. House. Committee on Banking - 1980 - 199 pages. Page 157 - "... argue that in a noninflationary situation with lower interest rates it should not — we should, consistent with price stability, have a minus number in M1."

This should show that in fact the phrase "minus number" is sometimes used to mean the same thing as "negative number". Its popularity may be due to having one less syllable.-R. S. Shaw 06:44, 23 March 2006 (UTC)

Wow, I'm surprised to see that in a technology book published in 2000. Well, again on Google book search, "minus numbers" gets 139 pages while "negative numbers" gets 14000 pages; they're not even on the same level. The relative authority of the books that show up in those two search results is also pretty evident to me. Melchoir 07:34, 23 March 2006 (UTC)

I saw (and corrected) a claim on the decimal page that +5 means "plus five" and -8 means "minus eight". I think that this should be mentioned on this page, just to tell people that it is incorrect. Also, I'm going to add a discussion of ^-.

Superscript notation

The article claims

In order to avoid confusion between the concepts of subtraction and negation, often the negative sign is written as a superscript:

I've not come across this before, so I'm a bit doubtful. I've seen the notation where a bar over the number represents negation, and I've seen various people write (well, define) negative numbers like this:

....99999 is -1 ....99998 is -2 ....99990 is -10

(particularly if you use some other symbol to mean "nines all the way to the left", this notation makes some things more consistent; it's also the equivalent of the two's-complement notation used by most computers).

But I can't see I've seen the negative sign as a superscript before, and if it's used "often", I should have. Is this specific to some education setting?

RandomP 14:09, 23 September 2006 (UTC)

I've seen it before, but it isn't done "often" in my estimation; it's rare, or at most occasional. I first saw it 30 years ago; it's used for negative numbers in the APL programming language. The APL documentation as I remember flogged the raised sign as a wonderful thing invented by Iverson for APL, but in my opinion it was mainly used because the APL syntax needed a separate symbol in order to be able to parse its expressions (which are unusual). I've never seen the raised minus in any context not connected with APL (except this article).

I think the usage in the article should be reduced to a single example, and the "often" changed. -R. S. Shaw 18:59, 23 September 2006 (UTC)

I believe the raised sign is pretty common in early education, where the target audience is easily confused. Melchoir 19:11, 23 September 2006 (UTC)

I think it looks really odd and should be changed. With proper use of brackets and/or multiplication symbols I don't see how confusion could arise. --CompuChip 09:53, 24 November 2006 (UTC)

I agree with Melchoir, the superscript notation is usefull in early education where "#--#" could easy confuse a person (I've found that "#-(-#)" doesn't help much). In many contexts, a shorter dash for negation verses subtraction is used (like on calculators). The superscript notation also serves to keep the signs distinct (so they don't appear to be the same dash).

A question on terminology

I am a native Dane, but teach math in English at highschool level. I have a problem with terminology.

In Danish, "-5" and "-x" are read aloud as "minus fem" and "minus x", not "negativ fem" and "negativ x". How's that in English?

Many students would read "-5" as "negative 5", but that's nonsense to me as 5 is not negative. I.e., I understand "negative as a property, and 5 does not have that property. Am I right?

Also, many students would read "-x" as "negative x", but again, I'd understand that as "a negaitve x" (i.e. x<0), and that's of course something else. Am I right? Or am I at least right to the extent that "negative x" would be ambiguous?--Niels Ø 14:07, 2 December 2006 (UTC)

Almost everyone says "minus x". A small number of people say "negative x" because they think it sounds cool or because they are acting in Hollywood movies. --Zero^talk 14:40, 2 December 2006 (UTC)

Thanks for the reply! Are there perhaps other opinions? How about "-5", is that also nearly always "minus 5"? When many of my students (being taught all over the World, and in many different languages, before I get them) say "negative 5" and "negative x", is that a primary school thing, or what?

And should some of this go into the article somehow?--Niels Ø 15:21, 2 December 2006 (UTC)

In my experience (American), both "minus 5" and "negative 5" are common, with "minus" more frequent, I'd guess mainly because it is a syllable shorter. "Negative 5" makes perfect sense to me, essentially being the name of the number 5 units less than zero. While "negative" is essentially always a property, "minus" seems more like the operator to me. "-" is always "minus" in "7 - 5", and "7 - ( - 5 )" would be "7 minus negative 5".

With an unknown, "-x", the situation is different because the "-" in that context is always an operator, never part of the name of a number. Thus with a variable it is almost always "minus", never "negative". For "y - (-x)" one might use "minus" for both, or maybe "the negation of" for the second "-". -R. S. Shaw 06:16, 3 December 2006 (UTC)

I'm a graduate from an American university and in my experience, "negative 5" is much more commonly used than "minus 5." At least, no mathematics professor I've ever had has ever used the term "minus" for anything but subtraction. Occasionally, a non-professional might use the term "minus" for that purpose, but very informally. Five away from zero, to the left, is NEGATIVE (not minus, unless you're in the 4th grade), five away from zero to the right is POSITIVE (not plus). -Laikalynx 03:06, 21 December 2006 (UTC)

That last comment is interesting. My experience is as a graduate student hearing lectures in theoretical physics at Oxford university in England, and everyone here says "minus 5". The word negative would be used to say that the quantity x is negative, if it equals minus 5. On the other hand, we say "6 minus minus 5 is 11", whereas in the usage of the last comment, we could say, more clearly, "6 minus negative 5 is 11". But if we really want to be that clear, we also have available "6 subtract minus 5 is 11". — Preceding unsigned comment added by 86.177.83.238 (talk) 09:03, 6 July 2011 (UTC)

It looks to me that the "-" is as part of the number as the "5." You wouldn't normaly break up other symbol combinations (like 23 becoming "two three" instead of "twenty-three"), so why seperate the negative sign. Also, in many contexts, negative (negation) and minus (subtration) use a different sign. — Jaxad0127 06:21, 24 January 2007 (UTC)

There cant be a -X. Say that was supposed to mean -9. The -9 is the variable. So that would be negative negative 9. There is no -(Random Variable Here) —The preceding unsigned comment was added by 65.80.7.142 (talk • contribs) 1:56, 9 July 2007 (UTC).

If -X was supposed to be -9, then X would be 9, not -9. Negating variable names is quite common and the basis for subtraction itself. — Jaxad0127 04:10, 16 July 2007 (UTC)

math

is 0.1 a non-negative number —Preceding unsigned comment added by 24.176.17.147 (talk) 20:53, 16 January 2008 (UTC)

Yes. FilipeS (talk) 14:01, 3 July 2008 (UTC)

it must be since it is higher than 0, any number higher than 0 is not negative 0.1 is 0 with .1 added so it is .1 above zero therefore .1 above being negative —Preceding unsigned comment added by 84.173.223.235 (talk) 07:13, 10 October 2008 (UTC)

Suggested move: Negative and non-negative number → Sign (mathematics)

Since Wikipedia prefers a single noun in titles. FilipeS (talk) 14:02, 3 July 2008 (UTC)

I don't think that should be done. The current title is a little clumsy, but does get closer to a clear statement of the subject. I'd prefer "Negative numbers" (or maybe "... number"); I presume this was previously used or at least discussed, and that the pedants won out and established the current title. -R. S. Shaw (talk) 06:29, 6 July 2008 (UTC)

Oppose The proposed title doesn't seem to be as clear as is the current one. And "Negative number(s)" is inappropriate, as the article covers both negative and positive numbers. Carl.bunderson (talk) 04:18, 9 July 2008 (UTC)

The Process of Causing Negative - Terminology

If I want to give the inverse of something (as in x changed to 1 / x) I am 'inverting' it. If I want to give the negative of something (as in x changed to -x) I am ... negatating it? ??? —Preceding unsigned comment added by 58.165.41.140 (talk) 05:15, 16 November 2008 (UTC)

"Negating" Jowa fan (talk) 03:50, 24 January 2010 (UTC)

Brahmagupta stated in Brahmasputhasiddhanta

Has anybody noticed these two paragraphs? Do they belong in the article? Katzmik (talk) 18:05, 14 January 2009 (UTC) More specifically, I was puzzled by the following contention:

"Great mathematicians such as Euler, Laplace and Cauchy were unable to provide a complete answer. Hermann Hankel proved using complex numbers that Brahmagupta was right"

Katzmik (talk) 18:08, 14 January 2009 (UTC)

It sounds like nothing more than overly flowery language to me. — Carl (CBM · talk) 18:35, 14 January 2009 (UTC)

I am puzzled by the implication that Euler, Laplace and Cauchy could not figure out something that brahmagupta did. Katzmik (talk) 18:42, 14 January 2009 (UTC)

I would be more concerned about exactly how Hankel proved it using complex numbers (maybe using polar form?). My guess is that the original author here meant to say that, before there were field-theoretic proofs that -1^2 = 1 and before there were concrete models of the negative numbers, it was difficult to justify why -1^2 = 1. A source for that opinion would be nice, though, so we can attribute it to somebody in particular. — Carl (CBM · talk) 18:59, 14 January 2009 (UTC)

It is just wrong. Euler for instance said - by - gave + just the same as + by + gave + and gave as reasoning that a single - by + gave -. And this idea of proof is a strange one too. It cannot be proved because it is a rule you are defining. It is perfectly easy to define funnymult where - funnymult - gives -. What one has to show is that a definition or set of axioms including -ve numbers and multiplication works out easier and more intuitive with the rule. The problems people like Carnot had were with the whole idea of an actual negative number existing. Dmcq (talk) 19:31, 14 January 2009 (UTC)

Great, I am glad someone more knowledgeable than myself stepped in. Please feel free to delete questionable material. Katzmik (talk) 19:35, 14 January 2009 (UTC)

It's trivial to prove that if 1 is the multiplicative identity of a field F then, in F, (-1)^2 = 1. I have no idea when the terminology necessary for this proof was developed. — Carl (CBM · talk) 19:50, 14 January 2009 (UTC)

I agree with Katzmik, this also seems quite bizarre to me. Parts of it are correct, Carnot did raise objections to negative numbers, and I have read places that Euler did not take the usual order on the numbers, putting negative numbers as larger than positive numbers. But I think he was adept at multiplying them. I will look through my history references in a day or two and try to put something more accurate. Unfortunately, I don't have the time today. Thenub314 (talk) 08:53, 15 January 2009 (UTC)

The historical information should be moved to the proper subsection. Bo Jacoby (talk) 09:23, 15 January 2009 (UTC).

The bit about Euler thinking negative numbers are greater than positive is probably from things like his -1 = 1 + 2 + 4 + 8 ... where he played round with formulae. It's that sort of explorative thinking that led to much of modern mathematics. Having a projective rather than absolute infinity is the same sort of thing. I can't imaging him having the least bit of a problem with negative numbers when he treated complex numbers so well! Dmcq (talk) 12:13, 16 January 2009 (UTC)

I'm fine with just removing the material under discussion until it's clarified. But I'll point out that it did not claim that Euler had any problem with complex numbers or negative numbers, only that he did not have a full explanation for why -1^2 = 1. For example, Argand diagrams (the plane model of complex numbers) were not introduced until after Euler's death. — Carl (CBM · talk) 13:06, 16 January 2009 (UTC)

I have an issue with the whole idea of proving -1^2 = 1. The formal construction section is much more correct I feel. Multiplication is extended to negative numbers in a straightforward and useful way. The result cannot be proved except as a result of the definition. At that rate we might as well say people didn't really understand negative numbers until he twentieth century and probably in the future mathematicians with their standards will say we didn't understand them. Dmcq (talk) 18:00, 16 January 2009 (UTC)

I removed the rubbish - the source book was pushing a viewpoint according to other books. I also removed the bit about proof and just said justification instead. Dmcq (talk) 12:57, 28 January 2009 (UTC)

Ironically we ran into an edit conflict. I was going to ask you what you fund odd about this proof:

In any ring, -1(-1+1) = 1· 0 = 0. But also -1(-1+1) = -1·-1 + -1·1= -1·-1 + -1. So -1·-1=1. The result for arbitrary products of negative numbers in an ordered ring follows by a sort of linearity, since -a = -1·a.

In what way is this "as the result of a definition"? To apply this to integers does not require that one know how the integers are defined, only that one believe that the integers satisfy enough of the axioms of an ordered ring. — Carl (CBM · talk) 13:03, 28 January 2009 (UTC)

You are defining that multiplication of negative numbers follows the rules of a ring. If we had that a times b is 0 if either a or b is negative that would also be consistent with the rules for the multiplication for non-negative numbers. It is because we want the rules for negative numbers to be nicer than that that they are defined the way they are. It isn't a question of belief. It is a question of justifying a definition. The only proving one could do is that saying it is a ring is consistent Dmcq (talk) 13:58, 28 January 2009 (UTC)

"If we had that a times b is 0 if either a or b is negative that would also be consistent with the rules for the multiplication for non-negative numbers." It would seem to violate that 1 is the multiplicative identity, or the rule that the product of two non-zero numbers is not zero.

It is true, I guess, one could say that because it isn't possible to use small blocks to visually represent multiplication of negative numbers, thus every fact about multiplication of negative numbers is up for grabs. But I think that's a pretty impoverished take on the role of intuition in understanding arithmetical operations. I expect that, however multiplication is "defined", 1 will be the multiplicative identity, the operation will be distributive, etc. — Carl (CBM · talk) 14:24, 28 January 2009 (UTC)

The original text and the citation I moved said Euler for instance didn't understand the product rule and that it was later proved. The book said it was only understood intuitively. That was just nonsense. What I wrote may not be very sensible but shows the idea of proof is just silly. It seems with you 'intuitive' understanding that you wouldn't qualify either! ;-) Dmcq (talk) 20:00, 28 January 2009 (UTC)

I think you're right about that. — Carl (CBM · talk) 21:03, 28 January 2009 (UTC)

Alternative Representation

I have fixed the part near the beginning where it says that in accounting negative numbers may be alternatively represented by placing them in parenthesis or writing them in red. An anonymous users, presumably not understanding the "alternative" part, added a sentence which said that negative numbers always must have a minus sign. This made the statement incorrect and contradictory. Chappell (talk) 22:15, 20 November 2009 (UTC)

Remove superscript minus

The article uses an overline minus to denote the negative sign. I don't believe that is in any way a common practice. I can see the good intent behind it but I don't believe wikipedia is supposed to set standards only reflect what is out there.

I therefore intend to replace these with a normal minus using a bracket if necessary to emphasise the number is a negative number. That is a convention I've seen a number of times. Any thoughts about that? Dmcq (talk) 11:18, 22 November 2009 (UTC)

Thanks Jowa fan, I had forgotten to get round to it. Dmcq (talk) 12:12, 24 January 2010 (UTC)

Plus and minus sign

I just noticed that the article does not mention the plus or minus signs. Not once. It's like a book written without using the letter 'e'. I think I'll break this very strange habit in the article. Dmcq (talk) 12:12, 24 January 2010 (UTC)

Split suggestion

Right now this article covers negative numbers, including their arithmetic and history, positive numbers, sign and its generalizations, the operation of negation, and so forth. This seems like far too many ideas for one article, and I propose splitting this article as follows:

• An article covering negative numbers, emphasizing their elementary properties.
• An article on the concept of sign in mathematics.
• A short article on the algebraic operation of negation.
• Possibly a short article on positive numbers or positivity (conceivably just a disambig page).

I have already created the first three proposed articles, using much of the material from this article:

• Negative number
• Sign (mathematics)
• Negation (algebra)

What do you think? Jim (talk) 21:59, 24 October 2010 (UTC)

I don't think much of the idea at all. It might be an idea to rename this article as Negative number, but I really don't see the point of the other two articles. So overall I think all three are superfluous. Dmcq (talk) 22:08, 24 October 2010 (UTC)

In some sense, what I am proposing is not very different from renaming this article to "Negative number", though I chose to frame the proposal as a split. The suggestion is to rename this article as well as relieve it from the burden of covering the general concept of sign. (Right now, part of the reason it needs the longer name is that this article covers both topics.) If you look at negative number and sign (mathematics), you can see what I'm proposing for the content of those two articles. Jim (talk) 22:51, 24 October 2010 (UTC)

The Sign (mathematics) article may have a point okay. I think negation should just point to negative number or perhaps the sign article or subtraction. I know the Plus and minus signs article distinguishes between negative number, negating and subtracting but I'm not certain an article is needed on all three - there a big bit in its talk page with people even disputing there a distinction between them. Dmcq (talk) 13:51, 31 October 2010 (UTC)

I agree that the Negation (algebra) article is the least important of the three, though I think it would be better to keep it. If you nominate it for deletion, we could ask the opinion of the folks on Wikipedia talk:WikiProject Mathematics. Jim (talk) 18:11, 31 October 2010 (UTC)

All three articles seem useful to me. Paul August ☎ 20:09, 31 October 2010 (UTC)

Requested move

I think my previous proposal was far too complicated to generate a consensus. Instead I am proposing a straightforward move:

Move?

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the move request was: page moved per discussion. A merge of some kind may be in order, but until that's decided, this seems to be a well-supported improvement to the name of this article. - GTBacchus^(talk) 01:26, 14 December 2010 (UTC)

---

Negative and non-negative numbers → Negative number — Relisted. Vegaswikian (talk) 02:55, 8 November 2010 (UTC) This title is much clearer, and will be less off-putting for mathematically unsophisticated readers. Most of the content of the article is about negative numbers, and non-negative numbers can be covered in other articles. Jim (talk) 01:18, 31 October 2010 (UTC)

• Nobrainer move - Slight rewording to the intro if it happens, tho. D O N D E groovily Talk to me 04:17, 31 October 2010 (UTC)

• Support. Paul August ☎ 07:01, 31 October 2010 (UTC)
• Support. Non-negative numbers get covered by the law of excluded middle. Diego Moya (talk) 12:59, 31 October 2010 (UTC)
• Support, yeah I hate unnecessarily long names. Dmcq (talk) 13:40, 31 October 2010 (UTC)
• Support. Nobrainer indeed. Hans Adler 22:34, 2 November 2010 (UTC)
  • Merging into sign (mathematics) per Amakuru is better. Hans Adler 11:52, 8 November 2010 (UTC)
• Move to "Positive and negative numbers". The article is about the feature of a number to be either positive or negative. It is not just about negative numbers. "Positive numbers" already redirects to this article. Vanjagenije 01:54, 4 November 2010 (UTC) Link to User:Vanjagenije and User talk:Vanjagenije are missing from user's signature and have been provided here

This kind of misses the point - the main problem with the current title is that is a wordy title for a subject with a short name. Your proposal has the same problem. D O N D E groovily Talk to me 02:38, 4 November 2010 (UTC)

Don't You think it would be kind of weired to move this article to "Negative number"? In that case "Positive number" would be redirect to "Negative number"! I don't think that's Ok. Vanjagenije 14:10, 4 November 2010 (UTC) Link to User:Vanjagenije and User talk:Vanjagenije are missing from user's signature and have been provided here

Kinda weird, sure, but it takes a person using the search box (for positive number) to the exact topic they're looking for, so I don't see a problem with it. D O N D E groovily Talk to me 14:32, 4 November 2010 (UTC)

• Oppose "non-negative" is the opposite of "negative" The law of excluded middle does not exclude the other half of the scale, this is not just about zero, its also about all the positive numbers as well. This article seems to cover negative numbers, non-negative numbers, positive numbers, non-positive numbers, and zero. I suggest positive, negative and zero 76.66.203.138 (talk) 04:49, 5 November 2010 (UTC)

The policy for article names WP:TITLE says they should be common names for the topic, not that they should describe it exactly. If one wanted to describe articles exactly one would start writing articles in te title. Dmcq (talk) 10:10, 5 November 2010 (UTC)

• Support in principle but Positive number must not redirect to Negative number. That would be ridiculous. We'll have to hive it off into a separate article if the move goes ahead.  — Amakuru (talk) 08:05, 8 November 2010 (UTC)
• Comment - I've just noticed that the whole article covers basically the same subject matter as Sign (mathematics), which is IMHO a more encyclopedic term than "Negative and non-negative numbers" anyway. The choice should (IMHO again) therefore be between merging all content from this article into that one and making all redirects point to Sign (mathematics), or splitting Negative number and Positive number into their own dedicated articles.  — Amakuru (talk) 08:10, 8 November 2010 (UTC)

  (Or, as a third choice, this article could be moved to Negative number with Positive number redirecting to Sign (mathematics)).  — Amakuru (talk) 08:12, 8 November 2010 (UTC)

• Comment - I've no problem with them both pointing at sign, but if negative number is kept I think positive number should point to it. The concept of a positive number only exists because of negative numbers, they'd just be 'numbers' with no qualification otherwise. Dmcq (talk) 13:15, 8 November 2010 (UTC)

  I'm not sure that the "complement of A only exists because A exists" argument is grounds for "complement of A" to be a redirect to "A". Obviously each case can be judged on its merits, but in general I find the logical fallacy of redirecting to an opposite to be worse than any perceived gain. For example, should Lesser ape be a redirect to Great ape, because the term "lesser ape" only exists to define those apes that are not great apes? And should Black and white television redirect to Color television because the only reason we refer to it as "black and white" is to differntiate it from the more modern color version? I wouldn't have thought so, in either case.  — Amakuru (talk) 14:53, 8 November 2010 (UTC)

The topics you indicated are interesting in themselves and have articles about them. Positive numbers aren't worth making an article about separate from negative numbers. The question is where positive number should point at. Dmcq (talk) 18:56, 8 November 2010 (UTC)

I would doubt that comment, since historically, there's been a belief amongst the common people that positive numbers are the only kind of numbers that really exist... although those people are also counting magnitudes as positive numbers. 76.66.203.138 (talk) 06:19, 13 November 2010 (UTC)

• Comment - I think that regardless of whether the renaming happens, positive should redirect to sign, not to this page. At the moment it looks as though negative is treated as the more fundamental concept, from which positive is derived. If anything, the reverse should be the case. Jowa fan (talk) 02:57, 11 November 2010 (UTC)

• Alternate proposal: Merge with Number line

  How about just merging this article into Number line? Right now that article is fairly short, and essentially duplicates what is in this one anyway. Number line, if interpreted broadly as anything related to the number line, including all numbers found on it, arguably includes everything covered in this article and discussed above. Then we would have Negative number, Positive number, Non-negative number and Non-positive number all redirect to the appropriate heading of that article, with each idea having its own concept briefly described, similar to what is done at Number. --Born2cycle (talk) 00:13, 8 December 2010 (UTC)

In fact, Sign (mathematics) could be merged/redirected into Number line too. --Born2cycle (talk) 00:15, 8 December 2010 (UTC)

• Support. The concept of a negative number certainly deserves an article, and the current title fails WP:PRECISION if this is to be that article. This is a much better way forward than any of the merge proposals IMO. A little refactoring would be good to support the move, and that will be more progress. Andrewa (talk) 17:07, 12 December 2010 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Lack of Detail in History

I have been investigating negative numbers in quadratic equations for a school project and I just can't sort out the history. Some people don't allow negative coefficients, and that means you can't have a single method of solution. Others don't use negative numbers in the calculations, which is almost the same thing. Others throw out any square roots of negative numbers, and others discard any negative solutions. All these things are different and clearly happened at various times in history but when and who committed them? For example, Brahmagupta used negative numbers, but does that mean he allowed negative coefficients? And he allowed negative solutions, it says in this article, which is an interesting comment because it almost implies that he had found both solutions, but I thought that had to wait for Bhaskara. I would like the article to sort this out. The quadratic equation is the most important historical use of the (non) use of negative numbers, so it represents a good focus. 86.177.83.238 (talk) 09:17, 6 July 2011 (UTC)QuadGirl

Misuse of sources

This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.

Please help by viewing the entry for this article shown at the page, and check the edits to ensure that any claims are valid, and that any references do in fact verify what is claimed.

I searched the page history, and found 13 edits by Jagged 85 (for example, see this edits). Tobby72 (talk) 16:38, 19 January 2012 (UTC)