Talk:Negative number

773:. 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, 215:

the evaluation of this expression not-a-number or impossible to evaluate, but the way it works is that with imaginary numbers, instead of even parity for signs, the signs are combined based on odd parity. Odd parity evaluates to negative when both signs are the same, the exact opposite of even parity. Odd parity versus even parity (which are calculated by XOR and XNOR) is the fundamental difference in sign combination rules between real and imaginary numbers. Sign combination rules are arbitrary and separate from the cardinal numbers in the operation. The sign amounts to a single binary digit as a second coordinate in a two dimensional phase space splitting the field into a complementary pair of 1 dimensional phase spaces in which the direction of addition is reversed. -10 - 10 is the same as -10 + - 10.

3260:

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.

5402:." The confusion in this is between the idea of "the opposite of a number" and "a number with an opposite value". If something is the opposite of a number, it is clearly not a number at all. A negative number is a number. It is a number whose value is the opposite of the value of a positive number, so when we add a negative and a positive number with the same absolute value, the sum is zero, the additive identity. It is absurd to say that the number that is negative is the "opposite of a number". The two numbers are opposites of each other, just as a left hand and a right hand are opposites of each other. To say that a left hand is the opposite of a hand would be absurd. 207:

consistency of these operations. One rule applies to both being positive, another rule when one is negative and the other positive, and a third rule if both are negative. The expression of sign as a binary vector matrix or compound value (like a coordinate space with a magnitude and a sign) is implied but for some reason not expressly stated. Also, it points to the fact that negative numbers are notional and time binding, that is, one can only practically demonstrate negative numbers either through reversal of the sequence of operations (see above where I illustrate the atomic subtraction operations implied in division) that is required when performing a division.

211:

parity of real numbers and odd parity of imaginary numbers in multiplication, division and exponents is about maintaining a consistent effect of the repeated addition of the factors. Odd parity in real numbers operations indicates an odd number of negative signs in the expanded atomic addition and subtraction that produces the multiplication/division/exponent, and gives you a negative result. Even parity gives you a positive result. As I mentioned in the previous paragraph, sign is really a one bit coordinate indicating the direction to perform the operation (subtract or add) grouped with the number attached to it.

5370:"The division between the rural life of the villages, where the Egyptian language was spoken, and the metropolis, where the citizens spoke Koine Greek and frequented the Hellenistic gymnasia, was the most significant cultural division in Roman Egypt, and was not dissolved by the Constitutio Antoniniana of 212, which made all free Egyptians Roman citizens.There was considerable social mobility however, accompanying mass urbanization, and participation in the monetized economy and literacy in Greek by the peasant population was widespread." 199:

functions in discrete logic arithmetic logic units, the logic operator XNOR (the negation of XOR) is applied to the sign bits of the two numbers being operated upon, an operation also called even parity, the result stored in the sign bit register, both are converted to the positive sign (usually indicated by 1 for positive or 0 for negative on the last bit of the byte/word/longword, the sequence of additions or subtractions performed and the sign bit altered at the end as determined beforehand by the even parity operation on the sign.

95: 3789:

the number line is because Descartes happened to write the positive numbers going to the right, and the opposite of right is left. The charge on the electron is negative because Ben Franklin happened to think electricity flowed in one direction, and the electrons actually flow in the opposite direction. When the electron was discovered by Thompson in 1897, more than a hundred years after Ben Franklin flew his kite, it was arbitrarily assigned a negative value just to make the commonly used equations work.

85: 64: 31: 4633:

never ever met anyone who had a problem understanding that "minus" can be a unary or a binary operator or even seeing a problem there, provided this person had at least some basic understanding of arithmetic. Then I started to watch YT math videos, and suddenly this phrase was everwhere. Can anyone tell me where it came from? It must have been "invented" by someone. (Probably an "education expert" who "discovered" it as a problem and forced it into (US?) schools…)

22: 3434:

the type of the account determining which does which. My own credit card statement lists reductions of the balance (such as refunds) with a "CR"; they are reductions in an asset of the bank. My checking statement lists refunds also as credits; they are increases in a liability of the bank. While I did slip up in my edit summary, the claim in the article is wrong.

1302:

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.

1495:. 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). 5327:

operations being presented. The arithmetic descriptions are for readers who need basic description for basic operations as an introduction or as a refresher. Using powers and roots is a level beyond the basic operations, and is not appropriate for the article, especially since it raises even further complications such as complex numbers. ---

4651:

and less in K through 12 (some states require they be lied do -- it's the law here in Tennessee, and I was lied to as long as I went to public schools. I had to go to a private school to lean the truth) I have to be careful to explain more and more basics. For example, I have to teach calculus students that 2/4 reduced to lowest terms is 1/2.

5349:"In Hellenistic Egypt, the Greek mathematician Diophantus in the 3rd century AD…" But the pages Hellenistic period and Ptolemaic Kingdom both agree that this period ends by 30 or 31 BC, three centuries before Diophantus. I am not enough of an historian and not sufficiently fluent in English to change this. Sorry to leave this to others. -- 2862:"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 599:. 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 4650:

I, also, as an undergraduate, was able to figure out the difference between an unary minus and a binary minus. But I was never taught the difference. Most of my students were never taught the difference, and some can't figure it out, so I explain it to them. But, as students in the US are taught less

4366:

can also be confusing. Since this is in a section trying to be more formal, we should try to do better. The subsection is also problematic in that it invokes some axiom from some unnamed system of axioms (and, like me, you may have doubts that the statement is simply a reiteration of an axiom). To

4246:

be its negative." This naturally leads to confusion, since not every number has a "negative" which is negative. For example, if we say "negative negative ten", that describes positive ten, but students naturally get confused being told that the "negative" of a negative is positive. On the other hand,

4065:

This is a point often badly taught in grade school and still misunderstood by some college students. A negative number represents the opposite of a positive number. If, for example, +10 represents a ten dollar profit, then -10 represents a ten dollar loss. The reciprocal is not an opposite. 1/10 does

3700:

Looks like no opinions either way are forthcoming from that project. I take the position that (1) accounting sources are relevant to an example headed "Finance" that uses accounting terminology and (2) a subjective feeling that text is accurate contrary to sources is not a proper reason to keep it in

3556:

Again, the text in question makes a claim about how transactions are reported on an account statement. It's a claim about accounting. You can't just declare it accurate in some other imaginary domain. You've offered a source that says credits can be indicated by a minus sign, which is true (sometimes

3433:

But as for the claim of negative debits on a card: There is no such thing in accounting. The terminology and methods of accounting predate the acceptance of negative numbers. There are debits and credits, both positive. For any given account, one decreases the balance and the other increases it, with

2079:

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

1617:

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

1417:

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

1335:

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

194:

Explaining sign interactions in multiplication, division and exponential functions cannot be entirely illustrated by concrete examples. The resultant sign from multiplication when both are positive or one is positive and the other is negative can be illustrated so long as one uses the positive factor

4069:

An opposite is not the same as negative, as the writer above knows and says. If a number is positive, then the negative number with the same absolute value is its opposite. But just as the opposite of a positive number is a negative number, the opposite of a negative number is a positive number. And

3788:

In any case, Knowledge relies on standard sources, and the math books I teach out of define a negative number as an opposite. Knowledge of the number line seems to me slightly more advanced, known mainly to people who have taken some math in college. The reason the negative numbers go to the left on

3762:

To me, the idea of "less than" seems more primitive/intuitive than "opposite". Everyone knows (and has always known, it would seem to me) that one apple is less than two apples. And in fact if we want to know how much more three apples are than one, we take one apple away (i.e subtract) and see that

2471:

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

2248:

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

2173:

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

2046:

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

1958:

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

1792:

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

1534:

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

1436:

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

1014:

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

995:

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

757:

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

4598:

Clearly, many people have strong opinions on this subject, but as a teacher, I find that using "opposite" for "additive inverse" and "reciprocal" for "multiplicative inverse" help students to understand mathematics. To give just one example, to teach the quadratic formula as "The opposite of b plus

4274:

opposite. A +$ 10 credit is the opposite of a –$ 10 debit: it restores the original balance. A reciprocal is another type of opposite. A ×2 doubling is the opposite of a ×½ halving: again, it restores the original value. Addition and multiplication implement "opposite" differently. Other, less

2061:

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

1627:

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

1602:

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

214:

Thus -8 is the same as -1 x 8, and when you explain it this way you see that it is no more artificial and beyond the construct of simple addition or its temporal obverse, subtraction, than the √-1 radical of imaginary numbers. The rule in real numbers of using even parity on sign combinations makes

210:

Negative numbers relate to either one of two things in multiplication/division/exponents, either the repeated subtraction of a division operation or the repeated addition of negative numbers (or subtraction of positive numbers) of a multiplication involving one negative number. The rule about even

3828:

Paul August would be hard put to figure out how an electron's charge is supposedly less than that of a proton. Or, how a south pole is less than a north pole. He says let us take a partially ordered set (without saying wher the set came from). I say, let us take a commutative group. No "less than"

3622:

Your understanding is based on reading something into the source that it doesn't say. A credit is an adjustment that represents money a party owes to someone else (so in a bank-mediated refund, money is due from the refunder, and then the bank, to the customer). A minus sign is stated because it's

2010:

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

1606:

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

999:

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

451:

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

202:

When both signs are negative, as for the example -8 ÷ -2, one cannot perform an operation without performing first a common factor elimination (of -1) or negation of the numbers on both sides of the operator, such as -8 ÷ -2 = -1 x 8 ÷ -1 x 2, but again, deriving a positive sign via even parity or

4632:

I studied mathematics and physics in the 1980ies, when I started to read and speak English in a scientific context, and worked in research until about 2010. I never ever met anyone at any confenrece or read any book or article that used the term "negative one" for -1 or "negative x" for -x. And I

3259:

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

3010:

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

1266:

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

1215:

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

1026:

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

424:

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

5326:

Beyond language issues, the approach of the presentation is not easy enough, and this should not go in. Additionally, I don't think a section on powers and roots should be added to the article, as that is more advanced than appropriate for the fully-spelled-out type of explanation of arithmetic

3956:

It highlights a way mathematics can deal with decreases, by treating them as increases of negative amount. If a formula describes the effect of an increase by n, substituting −n into the same formula often describes a decrease by n correctly. Could that idea be expressed more clearly but still

3784:

Of course, you are entitled to your opinion. But you ask the average person on the street if anything is less than zero, and see what they say. On the other hand, ask them a few opposites: the opposite of left, the opposite of up, the opposite of addition, and my bet is every one will be able to

3720:

The essential definition of a negative number is that it represents an opposite. The problem with using "less than" to define negative is that it is a circular definition. The definition of "less than", in most books, is that a < b if and only if a - b is negative. We need some idea of what a

1650:

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

1588:

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?

1369:

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

1286:

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

4594:

The correct technical term is "additive inverse", but the way negative numbers are used every day is to represent opposites: in finance and in temperature, to give just two common examples. In the Merriam-Webster Dictionary, the third definition of negative is "something that is the opposite or

4289:

Agree entirely. Negative numbers are not inherently "negative". They are just negations (opposites) of the numbers we chose to call positive. For example, the northern hemisphere has positive latitudes and the southern hemisphere has negative latitudes. It could well have been the other way. --

3627:

way of marking a credit, but it doesn't make the credit a "negative debit." Account statements are not a distinct field of knowledge. They are an application of accounting, and if you don't want me to talk about accounting, please suggest a subject and relevant sources that support the example.

1936:

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

1538:

I was once taught to write my signs as superscript in primary school, and warned that I'll probably only see it as a normal minus sign because typewriters (remember those?) couldn't do superscript. I was reading this page because I was starting to question my own recollection. This page could

1355:

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"

4354:

usages have a much greater chance of being evoked. What is the opposite of something? Nothing. What is the opposite of a number? A letter, er... a shortage, er... a fraction, ... What is the opposite of zero? Nonzero. (Oops, that's a problem: in some contexts, the opposite of zero is not

2300:

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

198:

In binary computation the multiply, divide and exponent operations are performed precisely as I show above, except instead of the reordering that I demonstrate in order to have a positive real number as the counter for the corresponding negative number to perform the calculation, integer math

1359:

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

2230:

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

670:

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...

206:

The fact that the rule for sign of the product of multiplication, division and exponents requires a second rule for the negative pair that is contrary to a simple and operation directly points at the fact that these operations on negative numbers are arbitrary and break from the fundamental

1301:

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.

178:

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

195:

to give the cardinal value to the implied repeated addition or subtraction operation, or in other words, -5 x 2 = -5 + -5 = -10, or 10 ÷ -2 = 10 - 2 - 2 - 2 - 2 - 2 = 0 (the answer being contained in the number of the negative numbers required to get the result of zero for division).

3495:

This is not an article on accounting, but it makes an uncited claim in the context of accounting. So to explain my removal of the claim, I have to talk about accounting. There is no distinction between the accounting position of a bank and what it puts on its statement. The statement

3685:

It's pretty bold to insist that the status quo has to be maintained for claims that are contradicted by published sources, and I don't believe that any policy requires that. However, the subheading is "Finance" so I have requested comment from WikiProject Finance & Investing.

437:

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

1079:, 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? 5368:, part of the Roman Empire but with local people speaking Egyptian or Greek. The literate mathematicians of the day were all writing in Greek (indeed my understanding is that most mathematical writing throughout the Roman Empire was in Greek). To quote that Roman Egypt article, 2379:

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:

4051:". Mathematics has other opposites, such as reciprocal as an opposite with respect to multiplication. Indeed, 'opposite' is not the same as 'negative', and some of the later sections discussing aspects of negative numbers need to use 'negative of' and not 'opposite of'. -- 3453:, where the amount you owe is represented as a "balance" (a positive number), a payment or refund is a negative quantity. This is with respect to the frame of reference of the statement. How the accountant of the bank might maintain their books is a different matter. 1281:

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.

827:

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. --

255:

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 :-)

1959:- 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. 2996:- 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. 661:

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. --

4085:

R. S. Shaw reverted my addition to the article, and restored a version based on his misunderstanding of the proof that every number has one and only one opposite. Here is what he wrote, and after I corrected what he wrote, he reverted my correction.

996:

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!

4039:

I think the introduction is excellent for using the "opposite" concept in introducing negative numbers. For someone who doesn't yet have a firm grasp on negative numbers, this approach is a very good way of helping them along with understanding.

2320:

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.

267:

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... --

497:

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

691:

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

533:

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.

3064:

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.

1411:

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

2139:

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

5417:

I wonder what other sources we can find with clear accessible definitions / explanations. I don't think the current "a negative number represents an opposite" is really the most obvious either. Maybe something like "In mathematics, a

3812:

that there is a number 1 less than 0 and another one 1 less than it and so on, in order to get negative integers. That is one way to do it of course. This is the conception of mathematics as an invention, which is frankly revisionist

331:

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. --

4343:. The word has very broad general application, and hence is very dependent on context. Its use in the lead works because the lead carefully sets the context, beginning with the simple statement that a negative number "represents 3816:

But negative numbers weren't invented. Long before there were any "negative" numbers, there was debt-numbers and asset-numbers, going-forward and going-backward, going-right and going-left, increasing and decreasing etc. It took a

2204:

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

1567:

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

2937:, 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 3557:

before and sometimes after the number, BTW); it doesn't say anything about negative debits. There's an edit war only to the extent that you're restoring a claim to the article that is directly contradicted by relevant sources.

3049:

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.

2815:

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)

2640:

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.

2508:

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.

1628:

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".

808:

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.

5305: 1476:(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). 2776:. 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) 3912:

My first experience of anything leading to a negative number was way back when I was in infants' school around year 1950; where we were told that the answer to an arithmetic problem such as "subtract 5 from 3" was

4304:

Numbers can map to the real world in different ways. Some are symmetrical and arbitrary: we could just as easily make south positive. Others aren't: I can own 100 books but not –100. Some fall in between: we

3284:). 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. 4599:

or minus the square root of the quantity b squared minus four ac, the whole thing over two a," helps students avoid mistakes that are all too common when the formula is taught "negative b plus or minus ... ".

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Opposite does have a definition. In every case, a minus sign represents an opposite, and I cited a dictionary reference. But the mathematical meaning of opposite is "additive inverse", so that is right, too.

4275:

common, interpretations of "opposite" exist too: consider positive integers as house numbers on a uniform street, where 1 is opposite 2, 3 opposite 4, etc. and crossing the street twice takes you back home.

2452:

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.

2133:

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 =

1469:

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:

865:

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

1210:

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

2324:

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?

4265:

Yes, "negative" is ambiguous here: 123 is the negative of –123, but 123 is not a negative number. We need an unambiguous synonym for the first sense, but "opposite" may not be the best choice. How about

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I think it could. I'll give it a try. Elsewhere in the article, the word "increase" always describes a change from a smaller number to a larger. For example, the change from - 10 to - 3 is an increase.

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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 :

5145: 3808:. There is a "primitive/intuitive" notion of less than within a positive domain (cardinals, ordinals, lengths, areas,...). But there is nothing "less than" 0 in those domains. You have to say, let us 4468: 4182: 2360:

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.

1374:

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.

1453:

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 .

1244:"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..." 3145:, 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 3721:

negative number means before we can understand how it is possible for anything to be less than zero, an idea that is counterintuitive. The clearest way to understand negatives is as opposites.

784:

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

4309:

say that a millionaire owes –1,000,000 but it's simpler not to. A few we get wrong, such as the charge on the electron. But, although the words are arbitrary, the concepts aren't. Numbers

675:. 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 3221:

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.

654:

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. --

151: 1829:

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? ???

3510:"By convention, accountants never enter negative numbers in accounting records. That is, a decrease in an asset is not effected by a 'negative debit entry' but rather by a credit entry." 1564:

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?

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If we search Knowledge 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.

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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

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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). -

2887:

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.

442:

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. --

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built on exploiting people's confusion on this subtle point.) My bank statements contradict the claim in the article, and as yet nobody has offered any source to verify it. From

2231:

understanding arithmetical operations. I expect that, however multiplication is "defined", 1 will be the multiplicative identity, the operation will be distributive, etc. — Carl

4043:

It can be carried too far, though. While "a negative number represents an opposite" is a good introduction, further along we need to remember that "a negative number represents

5030: 4906: 3870:", we need a set (and an operation). My example of {0,1,2,3} above would work well (with addition modulo 4). It's still true that 1<2 without a negative number in sight. 2080:

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.

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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

1423:

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.-

1406:

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."

1401:

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"

461:

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. --

1248:

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

873:

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".

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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.

425:

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.)

353:

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. ;) --

1887:"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" 1077: 1051: 5466: 1491:

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

2794:

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.

2535:

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

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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. —

1415: 4535:

Yes, we need a clear term which is to addition as reciprocal is to multiplication. I don't think there's a single word for that. The most common term seems to be

4020:

Wiktionary cites three sources, all extremely marginal. You can, these days, find a reference for almost anything. We need to limit ourselves to reliable sources.

1015:

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.

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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.

2011:

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.

1156:

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 : -->

3530:. We don't care about accounting conventions. This is a mathematics article, and this is a rather obvious mathematical fact. Please desist from edit warring. -- 3763:

there are two apples left. After one plays around with subtraction awhile the question arises what happens when you try to subtract b from a when a < b? For

1752:

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

1578:

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. --

762:

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. --

4313:

inherently positive or negative, and we can distinguish the two easily. For example, negative is the sign of the product of two numbers of differing signs.

2830:

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.

800:

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??

239:

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

2607:

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. -

342:

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?

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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?

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afford a separate section on notation, covering that and various financial notations and maybe other natural and artificial languages and some history. --

647:

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! --

1669:

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)

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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. --

203:

XNOR on the sign must still be performed, and the rules listed for multiplication and division include a logic operation on the signs of even parity.

3460:

concepts. The negative of a negative is positive. So, it doesn't make sense to argue whether something is absolutely positive or absolutely negative.

251:

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

4673:, I changed "opposite" to "additive inverse" in that passage. It is improper to use "opposite" there since it doesn't have a definition. Thanks to 3500:

the accounting position of the bank. What the customer would consider their asset (a deposit obligation) is stated as a bank liability. (There's a

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game shows?). It's heading in the direction of so many "popular culture" sections, where editors start playing "I spy" with the article subject.

4618:

and is positive if b<0. (In isolation, "minus" is also ambiguous, this time with subtraction, but the context clarifies its meaning here.)

315:-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.) 2536: 117: 5486: 5214: 4713: 3583:

A debit is the amount charged to your account. A credit is a payment made to reduce your debt. Credits are identified by a negative (—) sign.

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with the same assignment of true and false as real numbers. The relation of signs in multiplication (and division) also mirrors even and odd

3161:

all redirect to the appropriate heading of that article, with each idea having its own concept briefly described, similar to what is done at

1937:

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

225: 2504:

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

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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!

1603:

property, "minus" seems more like the operator to me. "-" is always "minus" in "7 - 5", and "7 - ( - 5 )" would be "7 minus negative 5".

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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. —

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because I knew negative and positive numbers sound like any number but zero, which is not the intent of this article. Any objection? --

364:

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. --

3887:

As for "negative" numbers, the concept isn't useful in this case since every element can be regarded as both positive and negative. --

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for negative numbers in the binary system, not of negative numbers themselves. What we desparately need however is a history section.

3324:

also referred to as XNOR if you define positive as true and negative as false. The exact opposite operation occurs when dealing with

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People don't use their languages correctly many times. But I think it is unnecessary to mention such misuses in too much detail. --

614:

I think it's fine where it is. The discussion of where zero falls is natural for an article called "negative and positive numbers".

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

1561:

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?

5456: 386:. They're not the same thing, after all. I don't expect to read about positive numbers in an article called "negative number". 5087: 3821:

to put the debt-numbers and asset-numbers along with zero into one whole and say, "let us call these things integers". He was

2577:

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

877:

To illustrate (and to give me some practice with tables, but don't tell anyone I wasn't perfect before), consider the space

3744:) set. This definition does not rely on negative numbers. Indeed, it works for sets such as {0,1,2,3} or temperatures in 3656:

It doesn't say "negative number" or "negative debit" and I wonder if you're even open to any constructive compromise here.

3748:

where negative numbers do not occur, and even for applications such as alphabetical order where no numbers appear at all.

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My understanding is that a credit is a negative debit. What is your understanding? Why is a negative sign mentioned? --

1973:

Great, I am glad someone more knowledgeable than myself stepped in. Please feel free to delete questionable material.

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For exponent with negative index or root with negative degree, the result is their positive anwser’s inverse fraction.

3291:, and check the edits to ensure that any claims are valid, and that any references do in fact verify what is claimed. 3248:

Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

2598:

Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

1216:

suggest to specify "nonnegative reals" or "nonnegative integer" etc. in order to get the "usual" (particular) meaning.

3926: 3288: 3281: 1148: 3575:" (imaginary domain?). Minus sign is indeed used to indicate a negative number. The exact statement in the source is: 1922:

I am puzzled by the implication that Euler, Laplace and Cauchy could not figure out something that brahmagupta did.

5364:

I am also not enough of an expert to feel confident about the precise terminology used by historians. But this was

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if we say "the opposite of an opposite is the number we started with", most people find that easy to understand.

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This article has been edited by a user who is known to have misused sources to unduly promote certain views (see

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Added rules for division (in quite simplistic terms, since this is the same as multiplication -- same sign -: -->

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More confusion about negative numbers, which I've had to revert twice. The edit I have twice reverted says "In

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I believe the raised sign is pretty common in early education, where the target audience is easily confused.

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The relationship between rules of sign in multiplication, division and exponent operations and Boolean logic

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It’s because multiplying any negative numbers for odd number times, there is always one negative sign left

4367:

reduce the problems, I suggest using the term "additive opposite" in this subsection, something like this:

1681: 1389: 1203:) the meaning of "not negative" and is thus invariably defined once "negative" is defined. For example, an 850:

is usually neither negative nor positive nor 0. In order of increasing generality, the possibilities are:

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is grammatically better. Still, I rather prefer seperate articles for them, all linking to one another...

4731:

As base of exponent, if the index is even, it will be positive. If the index is odd, it will be negative

4002: 3942: 2916:. That would be ridiculous. We'll have to hive it off into a separate article if the move goes ahead. — 3858: 3775: 3741: 3481: 2823: 2783: 2686: 2635: 2563: 2417:

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

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negative." Since a is greater than b means (by defenition of order, whether it's total or partial) that

595:

But what about "I don't expect to read about positive numbers in an article called "negative number" by

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

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No inconsistency. You got the definition of greater wrong. What you put in was greater than or equal.

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You are defining that multiplication of negative numbers follows the rules of a ring. If we had that

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

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Its use in other, less explicit contexts can be problematic because the very wide range of general

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I think the usage in the article should be reduced to a single example, and the "often" changed. -

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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place. Anyone who thinks otherwise may go raise the issue in a Knowledge forum of their choice.

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hits, and all of them are coherently talking about negative numbers. But "minus numbers" gets

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numbers always must have a minus sign. This made the statement incorrect and contradictory.

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can't also exist separately. And maybe when all the material specific to those articles, to

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zero is its own opposite: a zero dollar profit is exactly the same as a zero dollar loss.

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reason it needs the longer name is that this article covers both topics.) If you look at

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negation of something else". Their definition of "reciprocal" does not mention opposite.

5435: 5373: 4974: 4678: 4291: 3888: 3845: 3830: 3643: 3589: 3531: 3464: 3055: 3001: 2933:- I've just noticed that the whole article covers basically the same subject matter as 2892: 2723: 2608: 2514: 2458: 2365: 2345: 2330: 2254: 2179: 2109: 2085: 2052: 2031: 2012: 1964: 1694: 1652: 1619: 1523: 1165: 1157:

and excludes the case of them being equal, greater than or equal corresponds to ≥. See

1101: 1011:, in French, and that this practice has spread through adoption of French terminology. 847: 789: 282: 240: 4979: 1219:

But if someone feels an inspiration, I strongly suggest to make the adequate changes.

5450: 4614:

I was taught "minus b plus or minus ...". I understood that the first "minus" means

4540: 3571:

The source is indeed talking about an account statement. Nowhere does it talk about "

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Yes. It sounds like there's many good reasons to leave this as a separate page. --

4339:

I think part of the above is showing some of the difficulty of using the bare word

4047:

opposite" is, more accurately, short for "a negative number represents an opposite

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since that had a bit of continuity with the intro and some seemed to think use of

547:. If possible, we certainly want to add about the history of negative numbers. -- 323:-3 × -4 = (-1 × 3) × (-1 × 4) = (-1 × -1) × (3 × 4) = 1 × 12 = 12, or more simply, 311:

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

263:

Makes sense to me. Follow the brackets carefully, Ed. negative * negative always

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Since negative number to the power of odd number will always be negative number

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The additive opposite of a number is unique, as is shown by the following proof.

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The rule about real number negatives exactly matches up with the truth table of

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I searched the page history, and found 13 edits by Jagged 85 (for example, see

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I definitely think that this should be discussed in an article linked to from

858:

with 0. The usual terminology is positive, negative, zero, as in the article.

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It's increasingly common in mathematics to distinguish, in general, between

1871:

Has anybody noticed these two paragraphs? Do they belong in the article?

846:

objects, abolishing the slightly awkward term non-negative (for example, a

2062:

of complex numbers) were not introduced until after Euler's death. — Carl

5427: 3767:

the key idea is that negative numbers are the solutions of the equations

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Zero, the square root of zero, the cube root of zero, zero squared. ;) --

5441: 5411: 5379: 5358: 5336: 5321: 5300:{\displaystyle x^{-y}=x^{0-y}={\frac {x^{0}}{x^{y}}}={\frac {1}{x^{y}}}} 4973:

For even, there is no anwser for real number, however there is one with

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I agree with the above. And the example seem accurate and useful to me.

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Including a tricky example like this in fact illustrates that point. --

3443: 3415: 3400: 3351: 3310: 3269: 3230: 3201: 3174: 3115: 3074: 3059: 3036: 3005: 2984: 2958: 2925: 2896: 2874: 2846: 2810: 2762: 2743: 2727: 2710: 2689: 2675: 2650: 2611: 2566: 2548: 2518: 2489: 2480:, you can see what I'm proposing for the content of those two articles. 2462: 2446: 2369: 2349: 2334: 2310: 2275: 2258: 2243: 2183: 2152: 2113: 2089: 2074: 2056: 2039: 2020: 2005: 1982: 1968: 1949: 1931: 1917: 1899: 1880: 1860: 1844: 1819: 1802: 1787: 1767: 1746: 1730: 1704: 1662: 1643: 1622: 1611: 1596: 1582: 1572: 1548: 1526: 1513: 1502: 1485: 1441: 1427: 1392:

turns up several usages, some of which seem like they could be called a

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What do you think? Exponent and root is a key part of mathematic too.--

3449:

This is an article on mathematics, not accounting. In the context of a

1905:

It sounds like nothing more than overly flowery language to me. — Carl

1450: 744:(or whatever you want to call it), in which case it can be folded into 733: 693: 4347:

opposite" and then carefully describing in what way it is an opposite.

5423: 5399: 5312:

This explanation is not clear, therefore not suitable for Knowledge.

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The historical information should be moved to the proper subsection.

1774:

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

745: 672: 510: 2249:

you 'intuitive' understanding that you wouldn't qualify either! ;-)

2174:

only proving one could do is that saying it is a ring is consistent

1535:

keep the signs distinct (so they don't appear to be the same dash).

1418:

should, consistent with price stability, have a minus number in M1."

4383:

of a number as a value which when added to the number sums to zero.

687:

You seem to be correct about the computer representation (although

394:

There is no doubt they are not the same thing. How about the title

4109: 319:

Multiplication of two negative numbers yields a positive result:

636:

I revert new move since there seems no agreement with it yet. --

474:, and this article ("Negative and positive numbers") links to it. 452:

much less common today, but it's still important historically --

5431: 1200: 5204:{\displaystyle {\sqrt{8}}={\frac {1}{\sqrt{8}}}={\frac {1}{2}}} 4868:

As radicand of root, if the degree is odd, it will be negative

4250:

I hope this clears things up. I will restore my correct proof.

3287:

Please help by viewing the entry for this article shown at the

1199:

nonnegative can be defined as desired, but "non negative" has (

303:

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

4490:. Using the law of cancellation for addition, it is seen that 4358:

I agree that the phrasing "Let x be a number and let y be its

4208:. Using the law of cancellation for addition, it is seen that 1883:

More specifically, I was puzzled by the following contention:

1287:

means, I think you'll get an excellent response if you ask on

15: 2826:

are missing from user's signature and have been provided here

2786:

are missing from user's signature and have been provided here

4270:(in sense 1)? Better suggestions are welcome!A negative is 3998: 3217:

certainly deserves an article, and the current title fails

3090:- I think that regardless of whether the renaming happens, 374:

Hold on. I really don't think it makes much sense to merge

3106:

is derived. If anything, the reverse should be the case.

5140:{\displaystyle 5^{-2}={\frac {1}{5^{2}}}={\frac {1}{25}}} 482: 3426:

The examples section seems a bit excessive (not one but

2588:

The following discussion is an archived discussion of a

1053:, the first part of the definition tells us that, since 3527: 3512:

The example is not accurate, and therefore not useful.

3298: 3295: 3102:

is treated as the more fundamental concept, from which

2963:(Or, as a third choice, this article could be moved to 3098:, not to this page. At the moment it looks as though 2340:

Thanks Jowa fan, I had forgotten to get round to it.

1592:

And should some of this go into the article somehow?--

881:(that's just maths-speak for tuples of real numbers): 5217: 5152: 5090: 5038: 5002: 4982: 4950: 4914: 4874: 4791: 4737: 4708:

Adding Exponent and root onto the calculation section

4463:{\displaystyle x+y'=0,\quad {\text{and}}\quad x+y=0.} 4412: 4177:{\displaystyle x+y'=0,\quad {\text{and}}\quad x+y=0.} 4126: 3238:

The above discussion is preserved as an archive of a

1118: 1059: 1033: 777:

or something (I don't remember the current name). --

679:. The use of links where appropriate should suffice. 2659:- Slight rewording to the intro if it happens, tho. 112:, a collaborative effort to improve the coverage of 1473:....99999 is -1 ....99998 is -2 ....99990 is -10 708:Agreed. Could we have a simple page title back, ie 285:of a number by -1 changes its sign. This is called 5299: 5203: 5139: 5076: 5032:The formula for negative redicand with even index 5024: 4988: 4965: 4936: 4900: 4844: 4778: 4569:was good and perhaps essential in this passage. - 4462: 4176: 1124: 1071: 1045: 4362:" could be confusing to some, but using the word 4238:The problem begins with the first sentence. "Let 1778:Since Knowledge prefers a single noun in titles. 4561:, it being the conventional term, but went with 5477:Knowledge level-4 vital articles in Mathematics 2398:A short article on the algebraic operation of 740:is taken out, there'll be very little left of 3578: 1825:The Process of Causing Negative - Terminology 8: 700:(like its special position among rings). -- 4521:Any comments about this proposed change? -- 4502:is equal to any other additive opposite of 1867:Brahmagupta stated in Brahmasputhasiddhanta 696:would deal with the specific properties of 247:(3 + (-3)) · (-4) = 3 · (-4) + (-3) · (-4). 3456:More generally, negative and positive are 2697:. Non-negative numbers get covered by the 2388:, emphasizing their elementary properties. 1328:Terminology is important. It's time for a 58: 5289: 5280: 5269: 5259: 5253: 5238: 5222: 5216: 5191: 5180: 5171: 5158: 5153: 5151: 5127: 5116: 5107: 5095: 5089: 5067: 5062: 5049: 5039: 5037: 5003: 5001: 4981: 4949: 4919: 4913: 4885: 4875: 4873: 4824: 4805: 4790: 4764: 4751: 4736: 4438: 4411: 4152: 4125: 4066:not represent the opposite of a profit. 4034: 1117: 1058: 1032: 1007:. It is also worth mentioning that 0 is 470:A more detailed discussion is already in 2718:, yeah I hate unnecessarily long names. 2263:I think you're right about that. — Carl 1340:, and the other 2 are incomprehensible. 481:... hm... so that's like numbers except 5467:Knowledge vital articles in Mathematics 5077:{\displaystyle {\sqrt{-x}}=i{\sqrt{x}}} 3999:https://en.wiktionary.org/Talk:increase 1343:So I Google "negative numbers" with an 1188:"Division is similar to multiplication" 521:Good point. Why not? Any objection? -- 174:positive result, different signs -: --> 60: 19: 5422:represents the opposite of a positive 5369: 2949:into their own dedicated articles. — 2559:All three articles seem useful to me. 2537:Knowledge talk:WikiProject Mathematics 5482:B-Class vital articles in Mathematics 4845:{\displaystyle (-4)^{3}=-(4^{3})=-64} 1449:I saw (and corrected) a claim on the 326:-3 × -4 = -1 × (3 × -4) = -(-12) = 12 7: 3642:The source says "negative sign". -- 3528:bringing in "accounting conventions" 2603:The result of the move request was: 1289:Knowledge:Reference desk/Mathematics 509:Why not put all this information on 106:This article is within the scope of 4510:is the unique additive opposite of 3740:as a preceding b in an ordered (or 3422:Negative numbers in popular culture 2413:(conceivably just a disambig page). 1180:bad jokes and other non...negatives 49:It is of interest to the following 5492:High-priority mathematics articles 4396:be its additive opposite. Suppose 4220:is equal to any other negative of 1195:some comments on the folllowing : 1132:. HSNie 23:22, 30 May 2009 (UTC) 14: 4779:{\displaystyle (-5)^{2}=5^{2}=25} 4677:for the suggested correction. -- 3850:I think you've conflated some of 3506:Understanding the Financial Score 2619:Negative and non-negative numbers 601:negative and non-negative numbers 126:Knowledge:WikiProject Mathematics 5462:Knowledge level-4 vital articles 4400:is another additive opposite of 3188:could be merged/redirected into 129:Template:WikiProject Mathematics 93: 83: 62: 29: 20: 5025:{\displaystyle {\sqrt {-4}}=2i} 4901:{\displaystyle {\sqrt{-125}}=5} 4856:-3 × -4 × -5 = 3 × 4 × -5 = -60 3941:What does that exactly mean? -- 2774:"Positive and negative numbers" 1236:First usage of negative numbers 564:I would like to rename this to 146:This article has been rated as 5472:B-Class level-4 vital articles 5442:15:34, 12 September 2023 (UTC) 5412:10:31, 12 September 2023 (UTC) 4860:But if even, there is no left 4830: 4817: 4802: 4792: 4748: 4738: 3907:Whether negative numbers exist 2638:) 02:55, 8 November 2010 (UTC) 1715:is 0.1 a non-negative number 1514:19:11, 23 September 2006 (UTC) 1503:18:59, 23 September 2006 (UTC) 1486:14:09, 23 September 2006 (UTC) 1388:obscure. The first page of a 1231:13:16, 28 September 2005 (UTC) 1191:"If both have different signs" 1184:no comment on the following : 409:That would be better. Perhaps 1: 5398:represents the opposite of a 4443: 4436: 4355:nonzero but instead is zero.) 4157: 4150: 4030:12:34, 28 February 2022 (UTC) 4011:11:43, 27 February 2022 (UTC) 3711:18:04, 25 November 2019 (UTC) 3696:03:33, 20 November 2019 (UTC) 3666:03:07, 20 November 2019 (UTC) 3652:23:16, 19 November 2019 (UTC) 3638:20:46, 19 November 2019 (UTC) 3598:19:18, 19 November 2019 (UTC) 3567:18:21, 19 November 2019 (UTC) 3540:12:41, 19 November 2019 (UTC) 3522:20:24, 17 November 2019 (UTC) 3485:17:30, 17 November 2019 (UTC) 3473:11:05, 17 November 2019 (UTC) 3444:06:13, 17 November 2019 (UTC) 3231:17:07, 12 December 2010 (UTC) 3116:02:57, 11 November 2010 (UTC) 3075:06:19, 13 November 2010 (UTC) 2883:The policy for article names 2612:01:26, 14 December 2010 (UTC) 2391:An article on the concept of 2335:11:18, 22 November 2009 (UTC) 2311:22:15, 20 November 2009 (UTC) 1845:05:15, 16 November 2008 (UTC) 1623:03:06, 21 December 2006 (UTC) 1527:09:53, 24 November 2006 (UTC) 1277:03:18, 17 February 2006 (UTC) 1257:01:08, 11 February 2006 (UTC) 942:zero or positive or negative 479:Negative and positive numbers 411:Negative and positive numbers 120:and see a list of open tasks. 5487:B-Class mathematics articles 5380:05:58, 23 January 2023 (UTC) 5359:10:37, 22 January 2023 (UTC) 4035:'Negative' versus 'opposite' 3986:12:52, 1 February 2022 (UTC) 3967:23:34, 31 January 2022 (UTC) 3951:22:10, 31 January 2022 (UTC) 3931:10:20, 5 December 2021 (UTC) 3401:19:42, 28 October 2014 (UTC) 3352:21:46, 23 January 2013 (UTC) 3311:16:38, 19 January 2012 (UTC) 3202:00:15, 8 December 2010 (UTC) 3175:00:13, 8 December 2010 (UTC) 3060:18:56, 8 November 2010 (UTC) 3037:14:53, 8 November 2010 (UTC) 3006:13:15, 8 November 2010 (UTC) 2985:08:12, 8 November 2010 (UTC) 2959:08:10, 8 November 2010 (UTC) 2926:08:05, 8 November 2010 (UTC) 2897:10:10, 5 November 2010 (UTC) 2875:04:49, 5 November 2010 (UTC) 2847:14:32, 4 November 2010 (UTC) 2811:02:38, 4 November 2010 (UTC) 2763:11:52, 8 November 2010 (UTC) 2744:22:34, 2 November 2010 (UTC) 2728:13:40, 31 October 2010 (UTC) 2711:12:59, 31 October 2010 (UTC) 2690:07:01, 31 October 2010 (UTC) 2676:04:17, 31 October 2010 (UTC) 2651:01:18, 31 October 2010 (UTC) 2567:20:09, 31 October 2010 (UTC) 2549:18:11, 31 October 2010 (UTC) 2519:13:51, 31 October 2010 (UTC) 2490:22:51, 24 October 2010 (UTC) 2463:22:08, 24 October 2010 (UTC) 2447:21:59, 24 October 2010 (UTC) 2405:Possibly a short article on 2370:12:12, 24 January 2010 (UTC) 2350:12:12, 24 January 2010 (UTC) 2276:21:03, 28 January 2009 (UTC) 2259:20:00, 28 January 2009 (UTC) 2244:14:24, 28 January 2009 (UTC) 2184:13:58, 28 January 2009 (UTC) 2153:13:03, 28 January 2009 (UTC) 2114:12:57, 28 January 2009 (UTC) 2090:18:00, 16 January 2009 (UTC) 2075:13:06, 16 January 2009 (UTC) 2057:12:13, 16 January 2009 (UTC) 2040:09:23, 15 January 2009 (UTC) 2021:08:53, 15 January 2009 (UTC) 2006:19:50, 14 January 2009 (UTC) 1983:19:35, 14 January 2009 (UTC) 1969:19:31, 14 January 2009 (UTC) 1950:18:59, 14 January 2009 (UTC) 1932:18:42, 14 January 2009 (UTC) 1918:18:35, 14 January 2009 (UTC) 1900:18:08, 14 January 2009 (UTC) 1881:18:05, 14 January 2009 (UTC) 1861:03:50, 24 January 2010 (UTC) 1768:07:13, 10 October 2008 (UTC) 1731:20:53, 16 January 2008 (UTC) 1663:06:21, 24 January 2007 (UTC) 1612:06:16, 3 December 2006 (UTC) 1597:15:21, 2 December 2006 (UTC) 1583:14:40, 2 December 2006 (UTC) 1573:14:07, 2 December 2006 (UTC) 939:zero or positive or negative 833:03:04, 6 February 2006 (UTC) 396:negative and positive number 299:-1 × (3 + 4) = -(3 + 4) = -7 234:22:51, 23 January 2013 (UTC) 187:"... you get the idea. ;) -- 5426:; together the two numbers 5337:19:36, 1 October 2022 (UTC) 5322:10:54, 1 October 2022 (UTC) 4722:04:37, 1 October 2022 (UTC) 4643:03:42, 3 October 2022 (UTC) 3884:And 2 < 1 since 2+3 = 1. 2864:positive, negative and zero 1318:12:51, 23 August 2010 (UTC) 896:"new expanded" terminology 883: 724:, I also see no reason why 579:would make more sense than 5508: 4937:{\displaystyle n^{3}=-125} 4703:12:00, 16 April 2022 (UTC) 4687:17:43, 15 April 2022 (UTC) 4661:14:18, 15 April 2022 (UTC) 4628:12:02, 15 April 2022 (UTC) 4609:11:33, 15 April 2022 (UTC) 4579:20:41, 15 April 2022 (UTC) 4553:22:57, 14 April 2022 (UTC) 4531:22:14, 14 April 2022 (UTC) 4323:18:19, 14 April 2022 (UTC) 4300:14:07, 14 April 2022 (UTC) 4285:12:18, 14 April 2022 (UTC) 4260:12:05, 14 April 2022 (UTC) 4228:is the unique negative of 4080:11:58, 14 April 2022 (UTC) 4061:18:46, 13 April 2022 (UTC) 3358:Question on correctness - 3021:Black and white television 2296:Alternative Representation 1688:) 1:56, 9 July 2007 (UTC). 1442:07:34, 23 March 2006 (UTC) 1428:06:44, 23 March 2006 (UTC) 1379:05:48, 23 March 2006 (UTC) 1240:From the current article: 775:political status of Taiwan 771:Computer numbering formats 760:Computer numbering formats 738:Computer numbering formats 689:Computer numbering formats 677:Computer numbering formats 587:seems overly complicated. 545:concept of negative number 4112:of the real number system 4100:be its negative. Suppose 3416:09:22, 8 April 2016 (UTC) 3255:Lack of Detail in History 1705:04:10, 16 July 2007 (UTC) 1554:A question on terminology 1549:11:31, 3 April 2012 (UTC) 1370:number". If anyone has a 822:01:38, Nov 18, 2004 (UTC) 792:15:04, 29 Sep 2003 (UTC) 145: 78: 57: 5345:Diophantus, Hellenistic? 4049:with respect to addition 3270:09:17, 6 July 2011 (UTC) 3245:Please do not modify it. 2595:Please do not modify it. 2316:Remove superscript minus 1820:04:18, 9 July 2008 (UTC) 1803:06:29, 6 July 2008 (UTC) 1788:14:02, 3 July 2008 (UTC) 1747:14:01, 3 July 2008 (UTC) 1644:09:03, 6 July 2011 (UTC) 1493:APL programming language 1296:17:50, 9 June 2006 (UTC) 1170:01:43, 31 May 2009 (UTC) 1106:23:03, 29 May 2009 (UTC) 1089:18:56, 29 May 2009 (UTC) 813:22:32, 17 Nov 2004 (UTC) 804:19:30, 6 Nov 2004 (UTC) 666:09:58 11 Jun 2003 (UTC) 591:00:08 22 May 2003 (UTC) 585:Negativity (mathematics) 572:22:57 21 May 2003 (UTC) 517:22:01 21 May 2003 (UTC) 506:21:51 21 May 2003 (UTC) 433:13:17 21 May 2003 (UTC) 390:13:03 21 May 2003 (UTC) 336:11:15 Dec 6, 2002 (UTC) 272:10:26 Dec 6, 2002 (UTC) 260:20:58 Dec 5, 2002 (UTC) 152:project's priority scale 4104:is another negative of 3897:16:41, 3 May 2021 (UTC) 3880:15:44, 3 May 2021 (UTC) 3862:15:25, 3 May 2021 (UTC) 3839:14:27, 3 May 2021 (UTC) 3799:11:35, 3 May 2021 (UTC) 3779:16:08, 2 May 2021 (UTC) 3758:12:09, 2 May 2021 (UTC) 3731:11:48, 2 May 2021 (UTC) 3360:Negative number#History 2755:per Amakuru is better. 1072:{\displaystyle 0\leq 0} 1046:{\displaystyle b\leq a} 1022:00:30, 1 May 2006 (UTC) 781:22:04 6 Jun 2003 (UTC) 766:21:30 11 Jun 2003 (UTC) 752:09:58 11 Jun 2003 (UTC) 716:18:56 6 Jun 2003 (UTC) 704:09:58 11 Jun 2003 (UTC) 683:16:39 6 Jun 2003 (UTC) 658:04:48 6 Jun 2003 (UTC) 651:04:42 6 Jun 2003 (UTC) 640:04:21 6 Jun 2003 (UTC) 633:04:14 6 Jun 2003 (UTC) 618:14:24 22 May 2003 (UTC) 607:02:24 22 May 2003 (UTC) 560:22:30 21 May 2003 (UTC) 551:22:27 21 May 2003 (UTC) 525:22:02 21 May 2003 (UTC) 493:19:25 21 May 2003 (UTC) 465:22:00 21 May 2003 (UTC) 456:19:30 21 May 2003 (UTC) 446:19:15 21 May 2003 (UTC) 417:13:11 21 May 2003 (UTC) 402:13:08 21 May 2003 (UTC) 357:11:18 Dec 6, 2002 (UTC) 346:11:32 Dec 6, 2002 (UTC) 109:WikiProject Mathematics 5457:B-Class vital articles 5301: 5205: 5141: 5078: 5026: 4990: 4967: 4938: 4902: 4846: 4780: 4464: 4178: 3854:, comments with mine. 3825:rather than inventing. 3771:= a-b where a < b. 3585: 2699:law of excluded middle 1437:pretty evident to me. 1347:, and this time I get 1126: 1073: 1047: 5302: 5206: 5142: 5079: 5027: 4991: 4968: 4939: 4903: 4847: 4781: 4465: 4179: 3451:credit card statement 2912:must not redirect to 2824:User talk:Vanjagenije 2784:User talk:Vanjagenije 1676:comment was added by 1384:The usage is not all 1127: 1125:{\displaystyle \geq } 1074: 1048: 603:? Sounds strange? -- 36:level-4 vital article 5215: 5150: 5088: 5036: 5000: 4980: 4966:{\displaystyle n=-5} 4948: 4912: 4872: 4864:-5 × -4 = 5 × 4 = 20 4789: 4735: 4410: 4392:be a number and let 4242:be a number and let 4124: 4096:be a number and let 3526:Once again, you are 3502:whole class of scams 3334:Parity (mathematics) 3282:WP:Jagged 85 cleanup 2906:Support in principle 2736:. Nobrainer indeed. 2506:Plus and minus signs 2384:An article covering 1457:Superscript notation 1250:negative temperature 1116: 1057: 1031: 974:"strictly negative" 132:mathematics articles 4557:I considered using 3213:. The concept of a 3159:Non-positive number 3155:Non-negative number 3094:should redirect to 2437:What do you think? 2356:Plus and minus sign 1461:The article claims 796:Classification of 0 296:-1 × -8 = -(-8) = 8 5297: 5201: 5137: 5074: 5022: 4986: 4963: 4934: 4898: 4842: 4776: 4460: 4444: 4437: 4174: 4158: 4151: 3391:correct? Thanks, 3379:third century A.D. 3186:Sign (mathematics) 3137:this article into 3123:Alternate proposal 2973:Sign (mathematics) 2939:Sign (mathematics) 2935:Sign (mathematics) 2752:sign (mathematics) 2533:Negation (algebra) 2502:Sign (mathematics) 2478:sign (mathematics) 2432:Negation (algebra) 2427:Sign (mathematics) 1390:Google Book search 1122: 1069: 1043: 910:strictly positive 893:"new" terminology 890:"old" terminology 844:strictlyt positive 472:Integral data type 175:negative result). 101:Mathematics portal 45:content assessment 5295: 5275: 5199: 5186: 5185: 5166: 5135: 5122: 5072: 5054: 5011: 4989:{\displaystyle i} 4890: 4727:Exponent and root 4563:additive opposite 4441: 4381:additive opposite 4155: 3937:Negative increase 3923:Anthony Appleyard 3919:5 won't go into 3 3868:commutative group 3742:partially ordered 3738:generally defined 3406:A.D. is correct. 3367:Hellenistic Egypt 3342:comment added by 3336:, respectively. 3326:imaginary numbers 3276:Misuse of sources 3015:be a redirect to 2839: 2827: 2803: 2787: 2668: 2639: 2531:I agree that the 2274: 2242: 2151: 2073: 2004: 1948: 1916: 1835:comment added by 1758:comment added by 1733: 1721:comment added by 1689: 1634:comment added by 1308:comment added by 1153: 1139:comment added by 993: 992: 871:partial preorders 224:comment added by 166: 165: 162: 161: 158: 157: 5499: 5386:Negative numbers 5306: 5304: 5303: 5298: 5296: 5294: 5293: 5281: 5276: 5274: 5273: 5264: 5263: 5254: 5249: 5248: 5230: 5229: 5210: 5208: 5207: 5202: 5200: 5192: 5187: 5184: 5176: 5172: 5167: 5165: 5154: 5146: 5144: 5143: 5138: 5136: 5128: 5123: 5121: 5120: 5108: 5103: 5102: 5083: 5081: 5080: 5075: 5073: 5071: 5063: 5055: 5053: 5048: 5040: 5031: 5029: 5028: 5023: 5012: 5004: 4995: 4993: 4992: 4987: 4972: 4970: 4969: 4964: 4943: 4941: 4940: 4935: 4924: 4923: 4907: 4905: 4904: 4899: 4891: 4889: 4884: 4876: 4865: 4857: 4851: 4849: 4848: 4843: 4829: 4828: 4810: 4809: 4785: 4783: 4782: 4777: 4769: 4768: 4756: 4755: 4672: 4559:additive inverse 4537:additive inverse 4469: 4467: 4466: 4461: 4442: 4439: 4426: 4404:. By definition: 4183: 4181: 4180: 4175: 4156: 4153: 4140: 3849: 3354: 3322:Logical equality 3247: 3025:Color television 3011:example, should 2844: 2837: 2836: 2820:User:Vanjagenije 2817: 2808: 2801: 2800: 2780:User:Vanjagenije 2777: 2673: 2666: 2665: 2626: 2597: 2407:positive numbers 2386:negative numbers 2375:Split suggestion 2264: 2232: 2188:"If we had that 2141: 2063: 1994: 1938: 1906: 1847: 1770: 1716: 1702: 1697: 1671: 1660: 1655: 1646: 1320: 1207:is not negative. 1205:imaginary number 1152: 1133: 1131: 1129: 1128: 1123: 1078: 1076: 1075: 1070: 1052: 1050: 1049: 1044: 884: 539:Then what about 241:distributive law 236: 134: 133: 130: 127: 124: 103: 98: 97: 87: 80: 79: 74: 66: 59: 42: 33: 32: 25: 24: 16: 5507: 5506: 5502: 5501: 5500: 5498: 5497: 5496: 5447: 5446: 5420:negative number 5396:negative number 5388: 5351:Dominique Meeùs 5347: 5285: 5265: 5255: 5234: 5218: 5213: 5212: 5148: 5147: 5112: 5091: 5086: 5085: 5041: 5034: 5033: 4998: 4997: 4978: 4977: 4946: 4945: 4915: 4910: 4909: 4877: 4870: 4869: 4866: 4863: 4858: 4855: 4820: 4801: 4787: 4786: 4760: 4747: 4733: 4732: 4729: 4714:218.250.135.170 4710: 4666: 4541:random citation 4419: 4408: 4407: 4133: 4122: 4121: 4037: 3939: 3909: 3843: 3718: 3424: 3383:Should this be 3363: 3344:109.149.204.234 3337: 3318: 3278: 3257: 3252: 3243: 3215:negative number 3151:Positive number 3147:Negative number 3133:How about just 2971:redirecting to 2969:Positive number 2965:Negative number 2947:Positive number 2943:Negative number 2941:, or splitting 2914:Negative number 2910:Positive number 2842: 2832: 2806: 2796: 2671: 2661: 2623:Negative number 2593: 2583: 2575: 2474:negative number 2422:Negative number 2395:in mathematics. 2377: 2358: 2318: 2298: 2196:is 0 if either 2165:is 0 if either 1869: 1830: 1827: 1776: 1753: 1713: 1700: 1695: 1672:—The preceding 1658: 1653: 1629: 1556: 1459: 1394:reliable source 1372:reliable source 1326: 1303: 1264: 1238: 1182: 1134: 1114: 1113: 1055: 1054: 1029: 1028: 798: 730:Positive number 726:Negative number 710:negative number 625:They're called 577:negative number 500:negative number 491:Dante Alighieri 384:Negative number 376:Positive number 355:Dante Alighieri 226:109.149.204.234 219: 171: 131: 128: 125: 122: 121: 99: 92: 72: 43:on Knowledge's 40: 30: 12: 11: 5: 5505: 5503: 5495: 5494: 5489: 5484: 5479: 5474: 5469: 5464: 5459: 5449: 5448: 5445: 5444: 5387: 5384: 5383: 5382: 5346: 5343: 5342: 5341: 5340: 5339: 5324: 5292: 5288: 5284: 5279: 5272: 5268: 5262: 5258: 5252: 5247: 5244: 5241: 5237: 5233: 5228: 5225: 5221: 5198: 5195: 5190: 5183: 5179: 5175: 5170: 5164: 5161: 5157: 5134: 5131: 5126: 5119: 5115: 5111: 5106: 5101: 5098: 5094: 5070: 5066: 5061: 5058: 5052: 5047: 5044: 5021: 5018: 5015: 5010: 5007: 4985: 4975:imaginary unit 4962: 4959: 4956: 4953: 4933: 4930: 4927: 4922: 4918: 4897: 4894: 4888: 4883: 4880: 4862: 4854: 4841: 4838: 4835: 4832: 4827: 4823: 4819: 4816: 4813: 4808: 4804: 4800: 4797: 4794: 4775: 4772: 4767: 4763: 4759: 4754: 4750: 4746: 4743: 4740: 4728: 4725: 4709: 4706: 4690: 4689: 4648: 4647: 4646: 4645: 4592: 4591: 4590: 4589: 4588: 4587: 4586: 4585: 4584: 4583: 4582: 4581: 4519: 4518: 4517: 4516: 4515: 4472: 4470: 4459: 4456: 4453: 4450: 4447: 4435: 4432: 4429: 4425: 4422: 4418: 4415: 4405: 4386: 4384: 4377: 4375: 4372: 4356: 4348: 4330: 4329: 4328: 4327: 4326: 4325: 4236: 4235: 4234: 4233: 4187: 4186: 4185: 4184: 4173: 4170: 4167: 4164: 4161: 4149: 4146: 4143: 4139: 4136: 4132: 4129: 4116: 4115: 4114: 4113: 4084: 4036: 4033: 4018: 4017: 4016: 4015: 4014: 4013: 4003:Backinstadiums 3991: 3990: 3989: 3988: 3970: 3969: 3943:Backinstadiums 3938: 3935: 3934: 3933: 3908: 3905: 3904: 3903: 3902: 3901: 3900: 3899: 3885: 3864: 3826: 3814: 3782: 3781: 3760: 3717: 3714: 3683: 3682: 3681: 3680: 3679: 3678: 3677: 3676: 3675: 3674: 3673: 3672: 3671: 3670: 3669: 3668: 3609: 3608: 3607: 3606: 3605: 3604: 3603: 3602: 3601: 3600: 3586: 3581:Debits/Credits 3576: 3547: 3546: 3545: 3544: 3543: 3542: 3490: 3489: 3488: 3487: 3461: 3454: 3423: 3420: 3419: 3418: 3382: 3373:mathematician 3362: 3356: 3317: 3314: 3277: 3274: 3256: 3253: 3251: 3250: 3240:requested move 3234: 3233: 3207: 3206: 3205: 3204: 3179: 3178: 3119: 3118: 3084: 3083: 3082: 3081: 3080: 3079: 3078: 3077: 3042: 3041: 3040: 3039: 2990: 2989: 2988: 2987: 2928: 2902: 2901: 2900: 2899: 2878: 2877: 2856: 2855: 2854: 2853: 2852: 2851: 2850: 2849: 2789: 2788: 2767: 2766: 2765: 2730: 2713: 2692: 2679: 2678: 2657:Nobrainer move 2617: 2615: 2601: 2600: 2590:requested move 2584: 2582: 2579: 2574: 2573:Requested move 2571: 2570: 2569: 2556: 2555: 2554: 2553: 2552: 2551: 2524: 2523: 2522: 2521: 2495: 2494: 2493: 2492: 2466: 2465: 2435: 2434: 2429: 2424: 2415: 2414: 2403: 2396: 2389: 2376: 2373: 2357: 2354: 2353: 2352: 2317: 2314: 2297: 2294: 2293: 2292: 2291: 2290: 2289: 2288: 2287: 2286: 2285: 2284: 2283: 2282: 2281: 2280: 2279: 2278: 2217: 2216: 2215: 2214: 2213: 2212: 2211: 2210: 2209: 2208: 2207: 2206: 2137: 2136: 2135: 2121: 2120: 2119: 2118: 2117: 2116: 2097: 2096: 2095: 2094: 2093: 2092: 2028: 2027: 2026: 2025: 2024: 2023: 1988: 1987: 1986: 1985: 1956: 1955: 1954: 1953: 1952: 1889: 1888: 1868: 1865: 1864: 1863: 1826: 1823: 1812:Carl.bunderson 1775: 1772: 1760:84.173.223.235 1750: 1749: 1712: 1709: 1708: 1707: 1666: 1665: 1615: 1614: 1604: 1586: 1585: 1555: 1552: 1532: 1531: 1530: 1529: 1517: 1516: 1506: 1505: 1496: 1467: 1466: 1458: 1455: 1447: 1446: 1445: 1444: 1431: 1430: 1421: 1420: 1419: 1413: 1407: 1402: 1325: 1324:Minus numbers? 1322: 1299: 1298: 1263: 1260: 1246: 1245: 1237: 1234: 1213: 1212: 1208: 1193: 1192: 1189: 1181: 1178: 1177: 1176: 1175: 1174: 1173: 1172: 1121: 1108: 1068: 1065: 1062: 1042: 1039: 1036: 991: 990: 985: 980: 976: 975: 972: 969: 966: 962: 961: 956: 953: 948: 944: 943: 940: 937: 934: 930: 929: 924: 921: 916: 912: 911: 908: 905: 902: 898: 897: 894: 891: 888: 875: 874: 867: 859: 848:complex number 836: 835: 824: 823: 815: 814: 797: 794: 768: 767: 754: 753: 706: 705: 668: 627:signed numbers 623: 622: 621: 620: 619: 609: 608: 562: 561: 553: 552: 536: 535: 529: 527: 526: 495: 494: 476: 475: 467: 466: 458: 457: 448: 447: 435: 427: 426: 421: 420: 419: 418: 404: 403: 372: 371: 370: 369: 368: 359: 358: 350: 349: 348: 347: 344:Chas zzz brown 329: 328: 327: 324: 317: 316: 309: 308: 301: 300: 297: 294: 283:Multiplication 279: 274: 253: 249: 248: 217: 192: 183:to a negative 170: 167: 164: 163: 160: 159: 156: 155: 144: 138: 137: 135: 118:the discussion 105: 104: 88: 76: 75: 67: 55: 54: 48: 26: 13: 10: 9: 6: 4: 3: 2: 5504: 5493: 5490: 5488: 5485: 5483: 5480: 5478: 5475: 5473: 5470: 5468: 5465: 5463: 5460: 5458: 5455: 5454: 5452: 5443: 5440: 5437: 5433: 5429: 5425: 5421: 5416: 5415: 5414: 5413: 5409: 5405: 5401: 5397: 5393: 5385: 5381: 5378: 5375: 5371: 5367: 5363: 5362: 5361: 5360: 5356: 5352: 5344: 5338: 5334: 5330: 5325: 5323: 5319: 5315: 5311: 5310: 5309: 5308: 5307: 5290: 5286: 5282: 5277: 5270: 5266: 5260: 5256: 5250: 5245: 5242: 5239: 5235: 5231: 5226: 5223: 5219: 5211:It’s because 5196: 5193: 5188: 5181: 5177: 5173: 5168: 5162: 5159: 5155: 5132: 5129: 5124: 5117: 5113: 5109: 5104: 5099: 5096: 5092: 5068: 5064: 5059: 5056: 5050: 5045: 5042: 5019: 5016: 5013: 5008: 5005: 4983: 4976: 4960: 4957: 4954: 4951: 4931: 4928: 4925: 4920: 4916: 4895: 4892: 4886: 4881: 4878: 4861: 4853: 4839: 4836: 4833: 4825: 4821: 4814: 4811: 4806: 4798: 4795: 4773: 4770: 4765: 4761: 4757: 4752: 4744: 4741: 4726: 4724: 4723: 4719: 4715: 4707: 4705: 4704: 4700: 4696: 4688: 4684: 4680: 4676: 4670: 4665: 4664: 4663: 4662: 4658: 4654: 4644: 4640: 4636: 4631: 4630: 4629: 4625: 4621: 4617: 4613: 4612: 4611: 4610: 4606: 4602: 4596: 4580: 4576: 4572: 4568: 4564: 4560: 4556: 4555: 4554: 4550: 4546: 4542: 4538: 4534: 4533: 4532: 4528: 4524: 4520: 4513: 4509: 4505: 4501: 4497: 4493: 4489: 4485: 4481: 4477: 4473: 4471: 4457: 4454: 4451: 4448: 4445: 4433: 4430: 4427: 4423: 4420: 4416: 4413: 4406: 4403: 4399: 4395: 4391: 4387: 4385: 4382: 4379:We define an 4378: 4376: 4373: 4371: 4370: 4369: 4368: 4365: 4361: 4357: 4353: 4349: 4346: 4342: 4338: 4337: 4336: 4335: 4334: 4333: 4332: 4331: 4324: 4320: 4316: 4312: 4308: 4303: 4302: 4301: 4297: 4293: 4288: 4287: 4286: 4282: 4278: 4273: 4269: 4264: 4263: 4262: 4261: 4257: 4253: 4248: 4245: 4241: 4231: 4227: 4223: 4219: 4215: 4211: 4207: 4203: 4199: 4195: 4191: 4190: 4189: 4188: 4171: 4168: 4165: 4162: 4159: 4147: 4144: 4141: 4137: 4134: 4130: 4127: 4120: 4119: 4118: 4117: 4111: 4107: 4103: 4099: 4095: 4091: 4090: 4089: 4088: 4087: 4082: 4081: 4077: 4073: 4067: 4063: 4062: 4058: 4054: 4050: 4046: 4041: 4032: 4031: 4027: 4023: 4012: 4008: 4004: 4000: 3997: 3996: 3995: 3994: 3993: 3992: 3987: 3983: 3979: 3974: 3973: 3972: 3971: 3968: 3964: 3960: 3955: 3954: 3953: 3952: 3948: 3944: 3936: 3932: 3928: 3924: 3920: 3916: 3911: 3910: 3906: 3898: 3894: 3890: 3886: 3883: 3882: 3881: 3877: 3873: 3869: 3865: 3863: 3860: 3857: 3853: 3847: 3842: 3841: 3840: 3836: 3832: 3827: 3824: 3820: 3815: 3811: 3807: 3804:I agree with 3803: 3802: 3801: 3800: 3796: 3792: 3786: 3780: 3777: 3774: 3770: 3766: 3761: 3759: 3755: 3751: 3747: 3743: 3739: 3735: 3734: 3733: 3732: 3728: 3724: 3715: 3713: 3712: 3708: 3704: 3698: 3697: 3693: 3689: 3667: 3663: 3659: 3655: 3654: 3653: 3649: 3645: 3641: 3640: 3639: 3635: 3631: 3626: 3621: 3620: 3619: 3618: 3617: 3616: 3615: 3614: 3613: 3612: 3611: 3610: 3599: 3595: 3591: 3587: 3584: 3582: 3577: 3574: 3570: 3569: 3568: 3564: 3560: 3555: 3554: 3553: 3552: 3551: 3550: 3549: 3548: 3541: 3537: 3533: 3529: 3525: 3524: 3523: 3519: 3515: 3511: 3507: 3503: 3499: 3494: 3493: 3492: 3491: 3486: 3483: 3480: 3476: 3475: 3474: 3470: 3466: 3462: 3459: 3455: 3452: 3448: 3447: 3446: 3445: 3441: 3437: 3431: 3429: 3421: 3417: 3413: 3409: 3405: 3404: 3403: 3402: 3398: 3394: 3390: 3386: 3380: 3376: 3372: 3368: 3361: 3357: 3355: 3353: 3349: 3345: 3341: 3335: 3331: 3327: 3323: 3315: 3313: 3312: 3308: 3304: 3300: 3297: 3292: 3290: 3285: 3283: 3275: 3273: 3271: 3267: 3263: 3262:86.177.83.238 3254: 3249: 3246: 3241: 3236: 3235: 3232: 3228: 3224: 3220: 3216: 3212: 3209: 3208: 3203: 3199: 3195: 3191: 3187: 3183: 3182: 3181: 3180: 3177: 3176: 3172: 3168: 3164: 3160: 3156: 3152: 3148: 3144: 3140: 3136: 3131: 3130: 3124: 3121: 3120: 3117: 3113: 3109: 3105: 3101: 3097: 3093: 3089: 3086: 3085: 3076: 3072: 3068: 3067:76.66.203.138 3063: 3062: 3061: 3057: 3053: 3048: 3047: 3046: 3045: 3044: 3043: 3038: 3034: 3030: 3026: 3022: 3018: 3014: 3009: 3008: 3007: 3003: 2999: 2995: 2992: 2991: 2986: 2982: 2978: 2974: 2970: 2966: 2962: 2961: 2960: 2956: 2952: 2948: 2944: 2940: 2936: 2932: 2929: 2927: 2923: 2919: 2915: 2911: 2907: 2904: 2903: 2898: 2894: 2890: 2886: 2882: 2881: 2880: 2879: 2876: 2872: 2868: 2867:76.66.203.138 2865: 2861: 2858: 2857: 2848: 2845: 2840: 2835: 2829: 2828: 2825: 2821: 2814: 2813: 2812: 2809: 2804: 2799: 2793: 2792: 2791: 2790: 2785: 2781: 2775: 2771: 2768: 2764: 2761: 2758: 2754: 2753: 2750:Merging into 2748: 2747: 2746: 2745: 2742: 2739: 2735: 2731: 2729: 2725: 2721: 2717: 2714: 2712: 2708: 2704: 2700: 2696: 2693: 2691: 2688: 2685: 2681: 2680: 2677: 2674: 2669: 2664: 2658: 2655: 2654: 2653: 2652: 2648: 2644: 2637: 2633: 2629: 2624: 2620: 2614: 2613: 2610: 2606: 2599: 2596: 2591: 2586: 2585: 2580: 2578: 2572: 2568: 2565: 2562: 2558: 2557: 2550: 2546: 2542: 2538: 2534: 2530: 2529: 2528: 2527: 2526: 2525: 2520: 2516: 2512: 2507: 2503: 2499: 2498: 2497: 2496: 2491: 2487: 2483: 2479: 2475: 2470: 2469: 2468: 2467: 2464: 2460: 2456: 2451: 2450: 2449: 2448: 2444: 2440: 2433: 2430: 2428: 2425: 2423: 2420: 2419: 2418: 2412: 2408: 2404: 2401: 2397: 2394: 2390: 2387: 2383: 2382: 2381: 2374: 2372: 2371: 2367: 2363: 2355: 2351: 2347: 2343: 2339: 2338: 2337: 2336: 2332: 2328: 2322: 2315: 2313: 2312: 2308: 2304: 2295: 2277: 2272: 2268: 2262: 2261: 2260: 2256: 2252: 2247: 2246: 2245: 2240: 2236: 2229: 2228: 2227: 2226: 2225: 2224: 2223: 2222: 2221: 2220: 2219: 2218: 2203: 2199: 2195: 2191: 2187: 2186: 2185: 2181: 2177: 2172: 2168: 2164: 2160: 2156: 2155: 2154: 2149: 2145: 2138: 2132: 2131: 2129: 2128: 2127: 2126: 2125: 2124: 2123: 2122: 2115: 2111: 2107: 2103: 2102: 2101: 2100: 2099: 2098: 2091: 2087: 2083: 2078: 2077: 2076: 2071: 2067: 2060: 2059: 2058: 2054: 2050: 2045: 2044: 2043: 2041: 2037: 2033: 2022: 2018: 2014: 2009: 2008: 2007: 2002: 1998: 1992: 1991: 1990: 1989: 1984: 1980: 1976: 1972: 1971: 1970: 1966: 1962: 1957: 1951: 1946: 1942: 1935: 1934: 1933: 1929: 1925: 1921: 1920: 1919: 1914: 1910: 1904: 1903: 1902: 1901: 1897: 1893: 1886: 1885: 1884: 1882: 1878: 1874: 1866: 1862: 1858: 1854: 1850: 1849: 1848: 1846: 1842: 1838: 1837:58.165.41.140 1834: 1824: 1822: 1821: 1817: 1813: 1809: 1805: 1804: 1800: 1796: 1790: 1789: 1785: 1781: 1773: 1771: 1769: 1765: 1761: 1757: 1748: 1744: 1740: 1736: 1735: 1734: 1732: 1728: 1724: 1723:24.176.17.147 1720: 1710: 1706: 1703: 1698: 1692: 1691: 1690: 1687: 1683: 1679: 1675: 1670: 1664: 1661: 1656: 1649: 1648: 1647: 1645: 1641: 1637: 1636:86.177.83.238 1633: 1625: 1624: 1621: 1613: 1610: 1605: 1601: 1600: 1599: 1598: 1595: 1590: 1584: 1581: 1577: 1576: 1575: 1574: 1571: 1565: 1562: 1559: 1553: 1551: 1550: 1546: 1542: 1541:217.140.96.21 1536: 1528: 1525: 1521: 1520: 1519: 1518: 1515: 1512: 1508: 1507: 1504: 1501: 1497: 1494: 1490: 1489: 1488: 1487: 1484: 1480: 1477: 1474: 1471: 1464: 1463: 1462: 1456: 1454: 1452: 1443: 1440: 1435: 1434: 1433: 1432: 1429: 1426: 1422: 1416: 1414: 1410: 1408: 1405: 1403: 1400: 1398: 1397: 1395: 1391: 1387: 1383: 1382: 1381: 1380: 1377: 1373: 1368: 1364: 1361: 1357: 1354: 1350: 1346: 1341: 1339: 1333: 1331: 1323: 1321: 1319: 1315: 1311: 1307: 1297: 1294: 1290: 1285: 1284: 1283: 1279: 1278: 1274: 1270: 1261: 1259: 1258: 1255: 1251: 1243: 1242: 1241: 1235: 1233: 1232: 1229: 1225: 1221: 1217: 1209: 1206: 1202: 1198: 1197: 1196: 1190: 1187: 1186: 1185: 1179: 1171: 1167: 1163: 1160: 1155: 1154: 1150: 1146: 1142: 1138: 1119: 1109: 1107: 1103: 1099: 1095: 1094: 1093: 1092: 1091: 1090: 1086: 1082: 1066: 1063: 1060: 1040: 1037: 1034: 1024: 1023: 1020: 1016: 1012: 1010: 1006: 1001: 1000:begin with). 997: 989: 986: 984: 981: 978: 977: 973: 970: 967: 964: 963: 960: 957: 954: 952: 949: 946: 945: 941: 938: 935: 932: 931: 928: 925: 922: 920: 917: 914: 913: 909: 906: 903: 900: 899: 895: 892: 889: 886: 885: 882: 880: 872: 868: 864: 863:partial order 860: 857: 853: 852: 851: 849: 845: 841: 834: 831: 826: 825: 821: 817: 816: 812: 807: 806: 805: 803: 795: 793: 791: 787: 782: 780: 776: 772: 765: 761: 756: 755: 751: 747: 743: 742:Signed number 739: 735: 731: 727: 723: 722:Signed number 720:While I like 719: 718: 717: 715: 711: 703: 699: 695: 690: 686: 685: 684: 682: 678: 674: 667: 665: 659: 657: 652: 650: 646: 641: 639: 634: 632: 628: 617: 613: 612: 611: 610: 606: 602: 598: 594: 593: 592: 590: 589:Michael Hardy 586: 582: 578: 573: 571: 567: 559: 555: 554: 550: 546: 542: 538: 537: 532: 531: 530: 524: 520: 519: 518: 516: 512: 507: 505: 501: 492: 488: 487: 486: 484: 480: 473: 469: 468: 464: 460: 459: 455: 450: 449: 445: 441: 440: 439: 434: 432: 423: 422: 416: 412: 408: 407: 406: 405: 401: 397: 393: 392: 391: 389: 385: 381: 377: 367: 363: 362: 361: 360: 356: 352: 351: 345: 341: 340: 339: 338: 337: 335: 325: 322: 321: 320: 314: 313: 312: 306: 305: 304: 298: 295: 292: 291: 290: 288: 284: 280: 277: 273: 271: 266: 261: 259: 252: 246: 245: 244: 242: 237: 235: 231: 227: 223: 216: 212: 208: 204: 200: 196: 191: 190: 186: 182: 176: 168: 153: 149: 148:High-priority 143: 140: 139: 136: 119: 115: 111: 110: 102: 96: 91: 89: 86: 82: 81: 77: 73:High‑priority 71: 68: 65: 61: 56: 52: 46: 38: 37: 27: 23: 18: 17: 5419: 5404:Rick Norwood 5395: 5389: 5348: 5314:Rick Norwood 4867: 4859: 4730: 4711: 4695:Rick Norwood 4691: 4675:Rick Norwood 4653:Rick Norwood 4649: 4601:Rick Norwood 4597: 4593: 4566: 4562: 4558: 4511: 4507: 4503: 4499: 4495: 4491: 4487: 4483: 4479: 4475: 4401: 4397: 4393: 4389: 4380: 4363: 4359: 4351: 4344: 4340: 4310: 4306: 4271: 4252:Rick Norwood 4249: 4243: 4239: 4237: 4229: 4225: 4221: 4217: 4213: 4209: 4205: 4201: 4197: 4193: 4105: 4101: 4097: 4093: 4083: 4072:Rick Norwood 4068: 4064: 4048: 4044: 4042: 4038: 4022:Rick Norwood 4019: 3978:Rick Norwood 3957:concisely? 3940: 3918: 3914: 3822: 3809: 3806:Rick Norwood 3791:Rick Norwood 3787: 3783: 3768: 3764: 3723:Rick Norwood 3719: 3703:73.71.251.64 3699: 3688:73.71.251.64 3684: 3658:73.71.251.64 3630:73.71.251.64 3624: 3623:used as one 3580: 3579: 3559:73.71.251.64 3514:73.71.251.64 3509: 3505: 3497: 3457: 3450: 3436:73.71.251.64 3432: 3427: 3425: 3408:Double sharp 3388: 3384: 3378: 3364: 3338:— Preceding 3330:Exclusive or 3319: 3293: 3286: 3279: 3258: 3244: 3237: 3219:WP:PRECISION 3214: 3210: 3142: 3134: 3132: 3126: 3122: 3103: 3099: 3087: 3023:redirect to 2993: 2930: 2905: 2859: 2833: 2797: 2773: 2769: 2749: 2733: 2732: 2715: 2694: 2662: 2656: 2627: 2616: 2604: 2602: 2594: 2587: 2576: 2436: 2416: 2378: 2359: 2323: 2319: 2299: 2201: 2197: 2193: 2189: 2170: 2166: 2162: 2158: 2029: 1890: 1870: 1828: 1807: 1806: 1791: 1777: 1751: 1714: 1668: 1667: 1630:— Preceding 1626: 1616: 1591: 1587: 1568:ambiguous?-- 1566: 1563: 1560: 1557: 1537: 1533: 1481: 1478: 1475: 1472: 1468: 1460: 1448: 1385: 1366: 1365: 1362: 1358: 1352: 1348: 1344: 1342: 1337: 1334: 1329: 1327: 1310:91.36.93.115 1300: 1280: 1265: 1247: 1239: 1218: 1214: 1194: 1183: 1025: 1017: 1013: 1002: 998: 994: 987: 982: 958: 950: 926: 918: 878: 876: 856:linear order 843: 839: 837: 802:66.245.1.229 799: 785: 783: 769: 750:Toby Bartels 707: 702:Toby Bartels 697: 669: 664:Toby Bartels 660: 653: 649:Toby Bartels 642: 635: 631:Toby Bartels 624: 597:User:Evercat 574: 563: 543:or even the 528: 508: 502:article. -- 496: 477: 436: 428: 373: 330: 318: 310: 302: 286: 281: 278: 275: 264: 262: 254: 250: 238: 220:— Preceding 218: 213: 209: 205: 201: 197: 193: 184: 180: 177: 172: 169:Through 2003 147: 107: 51:WikiProjects 34: 5392:mathematics 5366:Roman Egypt 4616:unary minus 4506:. That is, 4272:one type of 4224:. That is, 3866:To "take a 3856:Paul August 3819:Brahmagupta 3773:Paul August 3479:Paul August 3190:Number line 3143:Number line 3139:Number line 3129:Number line 3127:Merge with 2684:Paul August 2632:Vegaswikian 2561:Paul August 1851:"Negating" 1831:—Preceding 1754:—Preceding 1717:—Preceding 1678:65.80.7.142 1304:—Preceding 1135:—Preceding 1112:instead of 515:Minesweeper 380:Nonnegative 307:-5 = -1 × 5 293:-1 × 5 = -5 123:Mathematics 114:mathematics 70:Mathematics 5451:Categories 5329:R. S. Shaw 4669:R. S. Shaw 4571:R. S. Shaw 4523:R. S. Shaw 4053:R. S. Shaw 3829:there! -- 3736:a<b is 3716:Definition 3573:accounting 3375:Diophantus 3194:Born2cycle 3167:Born2cycle 3013:Lesser ape 2843:Talk to me 2807:Talk to me 2703:Diego Moya 2682:Support. 2672:Talk to me 2605:page moved 2411:positivity 1795:R. S. Shaw 1609:R. S. Shaw 1500:R. S. Shaw 1425:R. S. Shaw 1360:confused. 1269:deeptrivia 1262:Diophantus 1159:Inequality 581:negativity 566:negativity 541:negativity 276:Removing: 243:to work: 5436:jacobolus 5374:jacobolus 4679:Kautilya3 4292:Kautilya3 3889:Kautilya3 3846:Kautilya3 3831:Kautilya3 3644:Kautilya3 3590:Kautilya3 3532:Kautilya3 3465:Kautilya3 3272:QuadGirl 3184:In fact, 3017:Great ape 2834:D O N D E 2798:D O N D E 2663:D O N D E 2609:GTBacchus 2032:Bo Jacoby 2013:Thenub314 1620:Laikalynx 1524:CompuChip 1356:phrases. 1349:3,060,000 1267:numbers. 1009:"positif" 790:AxelBoldt 736:, and to 39:is rated 5434:. ..." – 4567:opposite 4474:And so, 4364:opposite 4360:negative 4352:opposite 4341:opposite 4268:negation 4192:And so, 4108:. By an 3915:won't go 3823:unifying 3813:history. 3785:answer. 3625:possible 3508:(2007): 3458:relative 3393:Marasama 3340:unsigned 3192:too. -- 3108:Jowa fan 3104:positive 3100:negative 3092:positive 2885:WP:TITLE 2838:groovily 2818:Link to 2802:groovily 2778:Link to 2667:groovily 2628:Relisted 2400:negation 2303:Chappell 1853:Jowa fan 1833:unsigned 1793:title. - 1756:unsigned 1719:unsigned 1686:contribs 1674:unsigned 1651:sign. — 1632:unsigned 1511:Melchoir 1439:Melchoir 1376:Melchoir 1306:unsigned 1293:Melchoir 1254:Melchoir 1149:contribs 1137:unsigned 1005:positive 971:negative 968:negative 955:negative 923:positive 907:positive 904:positive 887:Element 869:several 840:positive 786:numerals 558:Dwheeler 454:Dwheeler 287:negation 222:unsigned 4498:. Thus 4216:. Thus 3810:imagine 3377:in the 3303:Tobby72 3223:Andrewa 3211:Support 3135:merging 3088:Comment 3029:Amakuru 2994:Comment 2977:Amakuru 2951:Amakuru 2931:Comment 2918:Amakuru 2734:Support 2716:Support 2695:Support 1975:Katzmik 1924:Katzmik 1892:Katzmik 1873:Katzmik 1780:FilipeS 1739:FilipeS 1607:"-". - 1594:Niels Ø 1570:Niels Ø 1483:RandomP 1451:decimal 1211:values) 1019:RandomP 965:(-1,-1) 811:Henrygb 734:Integer 714:Tarquin 694:Integer 681:Mintguy 673:numbers 616:Evercat 415:Evercat 388:Evercat 366:Tarquin 334:Tarquin 270:Tarquin 258:Ed Poor 189:doshell 150:on the 41:B-class 5424:number 5400:number 4944:Solve: 4620:Certes 4545:Certes 4315:Certes 4277:Certes 3959:Certes 3917:" or " 3872:Certes 3852:Certes 3750:Certes 3746:Kelvin 3387:or is 3369:, the 3163:Number 2975:). — 2860:Oppose 2192:times 2161:times 1808:Oppose 1412:mean." 1353:17,000 979:(1,-1) 959:varies 947:(0,-1) 927:varies 746:Number 643:I was 575:To me 511:number 185:number 181:number 47:scale. 4307:could 4110:axiom 4092:"Let 3428:three 3371:Greek 3299:edits 2967:with 2760:Adler 2741:Adler 2581:Move? 2205:zero. 2134:-1·a. 1737:Yes. 1696:Jaxad 1654:Jaxad 1141:HSNie 1081:HSNie 933:(0,0) 915:(1,0) 901:(1,1) 866:used. 748:. -- 712:? -- 629:! -- 513:? -- 398:? -- 382:into 28:This 5432:zero 5408:talk 5394:, a 5355:talk 5333:talk 5318:talk 4718:talk 4699:talk 4683:talk 4657:talk 4639:talk 4624:talk 4605:talk 4575:talk 4549:talk 4527:talk 4388:Let 4319:talk 4296:talk 4281:talk 4256:talk 4076:talk 4057:talk 4026:talk 4007:talk 3982:talk 3963:talk 3947:talk 3927:talk 3893:talk 3876:talk 3835:talk 3795:talk 3754:talk 3727:talk 3707:talk 3692:talk 3662:talk 3648:talk 3634:talk 3594:talk 3563:talk 3536:talk 3518:talk 3469:talk 3440:talk 3412:talk 3397:talk 3389:A.D. 3385:B.C. 3348:talk 3307:talk 3296:this 3289:page 3266:talk 3227:talk 3198:talk 3171:talk 3165:. -- 3157:and 3112:talk 3096:sign 3071:talk 3056:talk 3052:Dmcq 3033:talk 3002:talk 2998:Dmcq 2981:talk 2955:talk 2945:and 2922:talk 2908:but 2893:talk 2889:Dmcq 2871:talk 2822:and 2782:and 2770:Move 2757:Hans 2738:Hans 2724:talk 2720:Dmcq 2707:talk 2647:talk 2636:talk 2545:talk 2515:talk 2511:Dmcq 2500:The 2486:talk 2476:and 2459:talk 2455:Dmcq 2443:talk 2393:sign 2366:talk 2362:Dmcq 2346:talk 2342:Dmcq 2331:talk 2327:Dmcq 2307:talk 2271:talk 2255:talk 2251:Dmcq 2239:talk 2180:talk 2176:Dmcq 2148:talk 2110:talk 2106:Dmcq 2086:talk 2082:Dmcq 2070:talk 2053:talk 2049:Dmcq 2036:talk 2017:talk 2001:talk 1979:talk 1965:talk 1961:Dmcq 1945:talk 1928:talk 1913:talk 1896:talk 1877:talk 1857:talk 1841:talk 1816:talk 1799:talk 1784:talk 1764:talk 1743:talk 1727:talk 1711:math 1701:0127 1682:talk 1659:0127 1640:talk 1580:Zero 1545:talk 1386:that 1367:Even 1338:verb 1330:rant 1314:talk 1273:talk 1228:Talk 1201:imho 1166:talk 1162:Dmcq 1145:talk 1102:talk 1098:Dmcq 1085:talk 936:zero 842:and 830:Foof 820:Taku 779:Taku 764:Taku 728:and 656:Taku 645:bold 638:Taku 605:Taku 570:Taku 549:Taku 523:Taku 504:Taku 463:Taku 444:Taku 431:Taku 400:Taku 378:and 230:talk 142:High 5439:(t) 5430:to 5428:sum 5377:(t) 4932:125 4882:125 4635:Hjm 4543:). 4440:and 4311:are 4154:and 3921:". 3365:In 3301:). 3242:. 2772:to 2643:Jim 2541:Jim 2482:Jim 2439:Jim 2409:or 2267:CBM 2235:CBM 2200:or 2169:or 2144:CBM 2066:CBM 1997:CBM 1941:CBM 1909:CBM 1224:MFH 1111:--> 429:-- 265:did 5453:: 5410:) 5357:) 5335:) 5320:) 5243:− 5224:− 5160:− 5133:25 5097:− 5043:− 5006:− 4996:. 4958:− 4929:− 4879:− 4840:64 4837:− 4815:− 4796:− 4774:25 4742:− 4720:) 4701:) 4685:) 4659:) 4641:) 4626:) 4607:) 4577:) 4551:) 4529:) 4494:= 4492:y′ 4486:+ 4482:= 4480:y′ 4478:+ 4458:0. 4398:y′ 4345:an 4321:) 4298:) 4283:) 4258:) 4232:." 4212:= 4210:y′ 4204:+ 4200:= 4198:y′ 4196:+ 4172:0. 4102:y′ 4078:) 4059:) 4045:an 4028:) 4009:) 4001:-- 3984:) 3965:) 3949:) 3929:) 3895:) 3878:) 3837:) 3797:) 3765:me 3756:) 3729:) 3709:) 3694:) 3664:) 3650:) 3636:) 3596:) 3565:) 3538:) 3520:) 3498:is 3471:) 3442:) 3414:) 3399:) 3381:. 3350:) 3309:) 3268:) 3229:) 3200:) 3173:) 3153:, 3149:, 3125:: 3114:) 3073:) 3058:) 3035:) 3004:) 2983:) 2957:) 2924:) 2895:) 2873:) 2726:) 2709:) 2701:. 2649:) 2630:. 2625:— 2621:→ 2592:. 2547:) 2539:. 2517:) 2488:) 2461:) 2445:) 2368:) 2348:) 2333:) 2309:) 2269:· 2257:) 2237:· 2182:) 2146:· 2112:) 2088:) 2068:· 2055:) 2042:. 2038:) 2019:) 1999:· 1981:) 1967:) 1943:· 1930:) 1911:· 1898:) 1879:) 1859:) 1843:) 1818:) 1801:) 1786:) 1766:) 1745:) 1729:) 1684:• 1642:) 1547:) 1396:: 1336:a 1332:. 1316:) 1291:. 1275:) 1252:. 1226:: 1222:— 1168:) 1151:) 1147:• 1120:≥ 1104:) 1087:) 1064:≤ 1038:≤ 861:a 854:a 809:-- 534:-. 485:. 256:-- 232:) 5406:( 5372:– 5353:( 5331:( 5316:( 5291:y 5287:x 5283:1 5278:= 5271:y 5267:x 5261:0 5257:x 5251:= 5246:y 5240:0 5236:x 5232:= 5227:y 5220:x 5197:2 5194:1 5189:= 5182:3 5178:8 5174:1 5169:= 5163:3 5156:8 5130:1 5125:= 5118:2 5114:5 5110:1 5105:= 5100:2 5093:5 5069:y 5065:x 5060:i 5057:= 5051:y 5046:x 5020:i 5017:2 5014:= 5009:4 4984:i 4961:5 4955:= 4952:n 4926:= 4921:3 4917:n 4896:5 4893:= 4887:3 4834:= 4831:) 4826:3 4822:4 4818:( 4812:= 4807:3 4803:) 4799:4 4793:( 4771:= 4766:2 4762:5 4758:= 4753:2 4749:) 4745:5 4739:( 4716:( 4697:( 4681:( 4671:: 4667:@ 4655:( 4637:( 4622:( 4603:( 4573:( 4547:( 4539:( 4525:( 4514:. 4512:x 4508:y 4504:x 4500:y 4496:y 4488:y 4484:x 4476:x 4455:= 4452:y 4449:+ 4446:x 4434:, 4431:0 4428:= 4424:′ 4421:y 4417:+ 4414:x 4402:x 4394:y 4390:x 4317:( 4294:( 4279:( 4254:( 4244:y 4240:x 4230:x 4226:y 4222:x 4218:y 4214:y 4206:y 4202:x 4194:x 4169:= 4166:y 4163:+ 4160:x 4148:, 4145:0 4142:= 4138:′ 4135:y 4131:+ 4128:x 4106:x 4098:y 4094:x 4074:( 4055:( 4024:( 4005:( 3980:( 3961:( 3945:( 3925:( 3913:" 3891:( 3874:( 3859:☎ 3848:: 3844:@ 3833:( 3793:( 3776:☎ 3769:x 3752:( 3725:( 3705:( 3690:( 3660:( 3646:( 3632:( 3592:( 3561:( 3534:( 3516:( 3482:☎ 3467:( 3438:( 3410:( 3395:( 3346:( 3305:( 3264:( 3225:( 3196:( 3169:( 3110:( 3069:( 3054:( 3031:( 3000:( 2979:( 2953:( 2920:( 2891:( 2869:( 2722:( 2705:( 2687:☎ 2645:( 2634:( 2564:☎ 2543:( 2513:( 2484:( 2457:( 2441:( 2402:. 2364:( 2344:( 2329:( 2305:( 2273:) 2265:( 2253:( 2241:) 2233:( 2202:b 2198:a 2194:b 2190:a 2178:( 2171:b 2167:a 2163:b 2159:a 2150:) 2142:( 2108:( 2084:( 2072:) 2064:( 2051:( 2034:( 2015:( 2003:) 1995:( 1977:( 1963:( 1947:) 1939:( 1926:( 1915:) 1907:( 1894:( 1875:( 1855:( 1839:( 1814:( 1797:( 1782:( 1762:( 1741:( 1725:( 1680:( 1638:( 1543:( 1345:s 1312:( 1271:( 1164:( 1143:( 1100:( 1083:( 1067:0 1061:0 1041:a 1035:b 988:? 983:? 951:? 919:? 879:R 698:Z 483:0 228:( 154:. 53::

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