Talk:Negative number

message: no comment on the following :
* "Division is similar to multiplication"
* "If both have different signs"
some comments on the folllowing :
* nonnegative can be defined as desired, but "non negative" has (imho) the meaning of "not negative" and is thus invariably defined once "negative" is defined. For example, an imaginary number is not negative.
* in the context of "nonnegative matrix" I think one should include not only links but also comments to what is commonly called a positive matrix (for which the associated quadratic form takes ony nonnegative values)
I don't want to impose my ideas and thus don't make changes since this might be controversal, and I risk to be too axiomatic: I would call nonnegative all elements that are not less than zero (in any group equipped with a partial order), so this is not always the same than "positive or zero"; and suggest to specify "nonnegative reals" or "nonnegative integer" etc. in order to get the "usual" (particular) meaning.
But if someone feels an inspiration, I strongly suggest to make the adequate changes. — MFH: Talk 13:16, 28 September 2005 (UTC)
thread_title:  bad jokes and other non...negatives 

message: From the current article:
:"Negative numbers were not well-understood until modern times. As recently as the 18th century, the Swiss mathematician Leonhard Euler believed that negative numbers were greater than infinity..."
This seems unfairly closed-minded. The convention that −1 < 1 is natural if you want an ordered group, but some uses of negative numbers demand a different ordering: see negative temperature. Melchoir 01:08, 11 February 2006 (UTC)
thread_title:  First usage of negative numbers 

message: Diophantus's rejecting 20x+4=0 as a meaningful equation is cited as an evidence of knowledge of negative numbers in Greece. This is absurd, since it is a clear evidence to the contrary. It's like saying that somebody rejecting square root of negative numbers is an evidence that he knows imaginary numbers. deeptrivia (talk) 03:18, 17 February 2006 (UTC)
replies: text: The short answer is yes, but the longer answer is long indeed. After all, what do you mean by "existence"? One construction of negative numbers is given by the "Formal construction of negative and non-negative integers" section of this article. If you want a thoughtful explanation of what it all means, I think you'll get an excellent response if you ask on Wikipedia:Reference desk/Mathematics. Melchoir 17:50, 9 June 2006 (UTC)
thread_title:  Diophantus 

message: is 0.1 a non-negative number  —Preceding unsigned comment added by 24.176.17.147 (talk) 20:53, 16 January 2008 (UTC)
replies: text: Yes. FilipeS (talk) 14:01, 3 July 2008 (UTC)
thread_title:   math 

message: Since Wikipedia prefers a single noun in titles. FilipeS (talk) 14:02, 3 July 2008 (UTC)
thread_title:  Suggested move: Negative and non-negative number → Sign (mathematics) 

message: If I want to give the inverse of something (as in x changed to 1 / x) I am 'inverting' it.
If I want to give the negative of something (as in x changed to -x) I am ... negatating it?
???  —Preceding unsigned comment added by 58.165.41.140 (talk) 05:15, 16 November 2008 (UTC)
replies: text: "Negating" Jowa fan (talk) 03:50, 24 January 2010 (UTC)
thread_title:  The Process of Causing Negative - Terminology 

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

message: The article uses an overline minus to denote the negative sign. I don't believe that is in any way a common practice. I can see the good intent behind it but I don't believe wikipedia is supposed to set standards only reflect what is out there.
I therefore intend to replace these with a normal minus using a bracket if necessary to emphasise the number is a negative number. That is a convention I've seen a number of times. Any thoughts about that? Dmcq (talk) 11:18, 22 November 2009 (UTC)
replies: text: Thanks  Jowa fan, I had forgotten to get round to it. Dmcq (talk) 12:12, 24 January 2010 (UTC)
thread_title:  Remove superscript minus 

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

message: Right now this article covers negative numbers, including their arithmetic and history, positive numbers, sign and its generalizations, the operation of negation, and so forth.  This seems like far too many ideas for one article, and I propose splitting this article as follows:
* An article covering negative numbers, emphasizing their elementary properties.
* An article on the concept of sign in mathematics.
* A short article on the algebraic operation of negation.
* Possibly a short article on positive numbers or positivity (conceivably just a disambig page).
I have already created the first three proposed articles, using much of the material from this article:
* Negative number
* Sign (mathematics)
* Negation (algebra)
What do you think? Jim (talk) 21:59, 24 October 2010 (UTC)
replies: text: I don't think much of the idea at all. It might be an idea to rename this article as Negative number, but I really don't see the point of the other two articles. So overall I think all three are superfluous. Dmcq (talk) 22:08, 24 October 2010 (UTC)
replies: text: In some sense, what I am proposing is not very different from renaming this article to "Negative number", though I chose to frame the proposal as a split.  The suggestion is to rename this article as well as relieve it from the burden of covering the general concept of sign.  (Right now, part of the reason it needs the longer name is that this article covers both topics.)  If you look at negative number and sign (mathematics), you can see what I'm proposing for the content of those two articles. Jim (talk) 22:51, 24 October 2010 (UTC)

text: The Sign (mathematics) article may have a point okay. I think negation should just point to negative number or perhaps the sign article or subtraction. I know the Plus and minus signs article distinguishes between negative number, negating and subtracting but I'm not certain an article is needed on all three - there a big bit in its talk page with people even disputing there a distinction between them. Dmcq (talk) 13:51, 31 October 2010 (UTC)
replies: text: I agree that the Negation (algebra) article is the least important of the three, though I think it would be better to keep it.  If you nominate it for deletion, we could ask the opinion of the folks on Wikipedia talk:WikiProject Mathematics. Jim (talk) 18:11, 31 October 2010 (UTC)

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

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

message: This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.
Please help by viewing the entry for this article shown at the page, and check the edits to ensure that any claims are valid, and that any references do in fact verify what is claimed. 
I searched the page history, and found 13 edits by Jagged 85 (for example, see this edits). Tobby72 (talk) 16:38, 19 January 2012 (UTC)
thread_title: Misuse of sources

message: The rule about real number negatives exactly matches up with the truth table of Logical equality also referred to as XNOR if you define positive as true and negative as false. The exact opposite operation occurs when dealing with imaginary numbers, which are based on the formula of the square root of a negative, and is identical to the truth table of Exclusive or with the same assignment of true and false as real numbers. The relation of signs in multiplication (and division) also mirrors even and odd Parity (mathematics), respectively.  — Preceding unsigned comment added by 109.149.204.234 (talk) 21:46, 23 January 2013 (UTC)
thread_title:  The relationship between rules of sign in multiplication, division and exponent operations and Boolean logic 

message: [...] In Hellenistic Egypt, the Greek mathematician Diophantus in the third century A.D.[...].
Should this be B.C. or is A.D. correct?  Thanks, Marasama (talk) 19:42, 28 October 2014 (UTC)
replies: text: A.D. is correct. Double sharp (talk) 09:22, 8 April 2016 (UTC)
thread_title:  Question on correctness - [[Negative number#History]] 

message: *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 "[it] won't go" or "5 won't go into 3". Anthony Appleyard (talk) 10:20, 5 December 2021 (UTC)
thread_title:  Whether negative numbers exist 

message: What does that exactly mean? --Backinstadiums (talk) 22:10, 31 January 2022 (UTC)
replies: text: 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 concisely?  Certes (talk) 23:34, 31 January 2022 (UTC)
replies: text: 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.  Rick Norwood (talk) 12:52, 1 February 2022 (UTC)
replies: text: https://en.wiktionary.org/wiki/Talk:increase --Backinstadiums (talk) 11:43, 27 February 2022 (UTC)
thread_title:  Negative increase 

message: What do you think? Exponent and root is a key part of mathematic too.--218.250.135.170 (talk) 04:37, 1 October 2022 (UTC)
replies: text: This explanation is not clear, therefore not suitable for Wikipedia. Rick Norwood (talk) 10:54, 1 October 2022 (UTC)
replies: text: 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 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.  ---R. S. Shaw (talk) 19:36, 1 October 2022 (UTC)
thread_title: Adding Exponent and root onto the calculation section

message: As base of exponent, if the index is even, it will be positive. If the index is odd, it will be negative
(-5)^{2}=5^{2} = 25
(-4)^{3}=-(4^{3})= -64
It’s because multiplying any negative numbers for odd number times, there is always one negative sign left
But if even, there is no left
As radicand of root, if the degree is odd, it will be negative
\sqrt[3]{-125} = 5
Since negative number to the power of odd number will always be negative number
n^{3}=-125
Solve:n=-5
For even, there is no anwser for real number, however there is one with imaginary unit i.
\sqrt{-4}=2i
The formula for negative redicand with even index
\sqrt[y]{-x} = i\sqrt[y]{x}
For exponent with negative index or root with negative degree, the result is their positive anwser’s inverse fraction.
5^{-2}=\frac{1}{5^2}=\frac{1}{25}
\sqrt[-3]{8}=\frac{1}{\sqrt[3]{8}} = \frac {1}{2}
It’s because
x^{-y}=x^{0-y}=\frac{x^0}{x^y}=\frac{1}{x^y}
::This explanation is not clear, therefore not suitable for Wikipedia. Rick Norwood (talk) 10:54, 1 October 2022 (UTC)
replies: text: 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 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.  ---R. S. Shaw (talk) 19:36, 1 October 2022 (UTC)
thread_title: Exponent and root

message: "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. --Dominique Meeùs (talk) 10:37, 22 January 2023 (UTC)
replies: text: I am also not enough of an expert to feel confident about the precise terminology used by historians. But this was Roman Egypt, 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,  –jacobolus (t) 05:58, 23 January 2023 (UTC)
thread_title:  Diophantus, Hellenistic? 

message: More confusion about negative numbers, which I've had to revert twice. The edit I have twice reverted says "In mathematics, a negative number represents the opposite of a number." 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. Rick Norwood (talk) 10:31, 12 September 2023 (UTC)
replies: text: 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 negative number represents the opposite of a positive number; together the two numbers sum to zero. ..." –jacobolus (t) 15:34, 12 September 2023 (UTC)
thread_title: Negative numbers