Talk:Plus–minus sign

Does anyone really read +/- as "give or take" ?

Of course people say "give or take" meaning something similar to this, but do people really read this symbol as that? I've never encountered it, and it says "citation required". Perhaps it should go.

(And writing this, I realise that the page doesn't mention the typewriter-convention of "+/-". —Preceding unsigned comment added by 86.7.19.134 (talk) 23:20, 5 March 2010 (UTC)

I have heard it pronounced as give or take, but never in a scientific/statistical context as the article suggests. I have updated the article to make it clear that give or take is a colloquial way to pronounce the symbol. - Zephyris _Talk 16:47, 23 March 2011 (UTC)

I love the plus-minus sign!!!! Weeeeeeee! 66.103.235.169 22:18, 22 March 2007 (UTC)

Then, may I recommend the interrobang‽--Joel 00:14, 23 June 2007 (UTC)

AGK loves the interrobang :) AGK (talk) 18:56, 20 February 2008 (UTC)

Use for standard error of the mean

In biology, or at least cell biology, it's common to use plus-minus to give the standard error of the mean for a variable. In a paper, you typically declare what you're doing in the methods section, so there's no ambiguity; it is different to practice in other fields, though.

And yes, this does mean we're effectively using 67% confidence limits. Sigh.

-- Tom Anderson 2008-01-29 2013 +0000 —Preceding unsigned comment added by 128.40.81.63 (talk) 20:13, 29 January 2008 (UTC)

Purple box added

For transparency, consensus-building purposes, I wish to make editors aware that I have added the purple box, with "±" depicted, to the article (diff). If there are any qualms or enquiries regarding my change, please feel free to discuss with me on my talk page, or below (NB, you might wish to drop me a note of any discussion ongoing here, at my talk page). Regards, AGK (talk) 18:56, 20 February 2008 (UTC)

I changed the font of plus-minus in purple box to separate the signs from each other. User: unregistered

Chess

Is it worth mentioning the use of this symbol in chess notation to mean "[clear] advantage for White", as in Punctuation_(chess)#Position_evaluation_symbols? -Phoenixrod (talk) 19:00, 7 August 2008 (UTC)

Digits of precision

All the examples are for large uncertainties on imprecise numbers. Can anyone point to a source describing the number of digits used in relation with more precise numbers. Lets say you get a result something like 3.14159265±0.0012345678, what would be the correct way to write this up? --Thorseth (talk) 15:09, 2 February 2011 (UTC)

An example like the one you gave, "3.14159265±0.0012345678", would not normally be seen as the error is large enough that many of the significant figures are irrelevant - it is rare that more than one or two significant figures would be included in the error. Notation you could use would be 3.1415±0.0012.

If you are referring to the problem of preceding zeroes the normal way would be to use scientific notation or more appropriate units to express the number, e.g. 1.24±0.03×10^-5 m or 12.4±0.3 μm. - Zephyris _Talk 16:57, 23 March 2011 (UTC)

Yes, this was my understanding too, but can it be put in the article without a reference? --Thorseth (talk) 21:36, 23 March 2011 (UTC)

This is so generally known that in my opinion a reference is not needed, but if you wanted to include one you could refer to any scientific journal in which a number of figures are quoted in this format. It is also worth pointing out that, using the above example, the notation "3.1415(12)" is also common. Ehrenkater (talk) 17:41, 24 March 2011 (UTC)

It entirely depends what you are doing. The article is about the symbol itself, not its application that much. In most scientific applications you would only give two significant places for error, and properly round up the value, i.e. 3.1416±0.0012. However, in some other aplications, like interval arithmetic, affine arithmetic, etc, it is plausible you would use way more precision for various reasons. 2A02:168:F609:0:7855:CA84:B8D8:C659 (talk) 19:38, 11 August 2019 (UTC)

In the minus/plus section

It's probably worth noting that, while the expression x±y∓z isn't ambiguous, the expression x±y±z is, since it doesn't determine whether the signs can be different or whether they have to be the same. — Preceding unsigned comment added by 82.6.96.22 (talk) 12:17, 25 May 2011 (UTC)

That isn't quite correct. In many cases x±y±z is totally fine and non ambiguous. It is quite common in science literature to for example write 51.21 ± 0.13 (systematic) ± 0.121 (random), which is to separate two errors, like bias, accuracy and resolution, or sample variance separately. It is usually fine and non-ambiguous. Errors can be combined by simply summing them up (taking maximums), or combining using assumption about underlying distribution of errors, i.e. if they are normal distributions, square root of sum of squares, is usual method of for example. In some text articles, you will see even more terms, and I did see astronomical articles with up to 10 ± terms. 2A02:168:F609:0:7855:CA84:B8D8:C659 (talk) 19:33, 11 August 2019 (UTC)

Multiply-divide sign?

There is a ⋇ 'DIVISION TIMES' (U+22C7) , \divideontimes in Latex AMS, which is somehow analogous for multiply/divide. It is useful when showing error factors (geometric standard deviation factor), in geometric means and their errors for example. And in other situations. I think it should be mentioned somehow here, or referenced. 2A02:168:F609:0:7855:CA84:B8D8:C659 (talk) 19:29, 11 August 2019 (UTC)

Not Additive inverse? What then?

@Deacon Vorbis:

In the article, the first meaning given for "±" is as follows:

• In mathematics, it generally indicates a choice of exactly two possible values, one of which is the negation of the other.

What's meant is that one is the additive inverse of the other. I replaced "negation" with "additive inverse" but you reverted my edit, asserting that "there's no need for the technical MOS:JARGON here." If you're right that there's no need, you do need to suggest another replacement, since "negation" absolutely will not do. Neither the definitions of "negation" in Wiktionary (q.v.) nor those in any of the three dictionaries supplying The Free Dictionary (American Heritage, Collins, and Random House) gives "additive inverse" or any equivalent as a meaning for "negation". I think that's adequate evidence that additive inverse is so rare a meaning of "negation" that a replacement is necessary — jargon if unavoidable, but preferably something else.

Perhaps "… exactly two possible values that sum to zero"?

Perhaps "… exactly two possible values with the same absolute value but opposite signs"?

If "absolute value" is also too technical, I suppose that one could substitute "magnitude", though that's really a term for size and negative numbers don't have sizes.

I really think that, in mathematics, "additive inverse" is the correct term. Yes, it's technical, but mathematics is technical. The ± symbol occurs in contexts like "√4 = ± 2", which is meaningful only if the reader is mathematically literate and therefore familiar with phrases like "additive inverse" and "absolute value". I welcome your suggestions, however, as to a better way of conveying the point.

Peter Brown (talk) 02:20, 15 January 2020 (UTC)

How about "one of which is the negative of the other"?Spitzak (talk) 04:43, 15 January 2020 (UTC)

I think "additive inverse" may be used commonly in US-based elementary and secondary school mathematics pedagogy but that in other contexts it comes across as overly pedantic and technical and that other terms are used instead. For instance, I tried searching Google scholar for "negation" "floating point" (to set a context where the meaning is likely to be the one discussed here rather than logical negation or other meanings) and found some 11700 hits, compared with 532 for "additive inverse" "floating point". That is, in academic works discussing floating point numbers, "negation" is used roughly 22x as often as "additive inverse". If we can find a natural way of using "negative" rather than "negation", that might be ok, but I worry that the word "negative" is likely to be interpreted as meaning the negation of the absolute value (i.e. make the number into a negative number if it isn't one already) rather than the number with the opposite sign. —David Eppstein (talk) 07:15, 15 January 2020 (UTC)

Sorry for the late reply; I'd gotten a bit busy yesterday. Anyway, that none of the dictionaries specifically use the terminology "additive inverse" isn't surprising, but they do lead to things like (depending on dictionary) "the act of negating", which then lead to appropriate definitions. I think keeping negation is completely fine, but as a compromise, including both would probably be okay: something like "... one of which is the negation (the additive inverse) of the other.". I'm usually all for precise terminology, but when a plain, non-technical word will do in a fairly non-technical article, I think it should be preferred. –Deacon Vorbis (carbon • videos) 14:10, 15 January 2020 (UTC)

It does not matter if the reader things "negative" means "minus the absolute value". One of the numbers is minus the absolute value, the other is the absolute value, so this still applies.Spitzak (talk) 16:20, 15 January 2020 (UTC)

Incidentally, while we're being pedantic, there are contexts in which "negation" remains valid while "additive inverse" is incorrect. In many types of computer arithmetic, for instance, there are values $x$ for which $x+(-x)$ can cause an arithmetic overflow rather than producing zero, so $-x$ is not really the additive inverse of $x$. —David Eppstein (talk) 17:16, 15 January 2020 (UTC)

My appeal to dictionaries has been misconstrued. Yes, it "isn't surprising" that dictionaries don't use the precise phrase "additive inverse" since it is technical, demonstrably rare, and arguably pedantic. However, assuming that what is under consideration is the additive inverse, it is a valid objection to the use of "negation" that reputable dictionaries don't use this phrase or any equivalent, but only terms that mean something quite different. (I don't think that an overflow on x + (−x) is relevant to the meaning.) On this basis, I disagree with David Eppstein' latest comment; −x is not the "negation" of x, whether or not it's the additive inverse.

You folks have persuaded me to abandon my advocacy of "additive inverse" as a replacement for "negation" — it is rare, technical, and perhaps pedantic. So neither "negation" nor "additive inverse" will do. A fortiori, "the negation (the additive inverse)" won't do either; "negation" doesn't have the intended meaning and we cannot eliminate pedantry by putting it in parentheses.

Spitzak suggests "one is the negative of the other." David Eppstein worried that this might be interpreted to mean that one is the additive inverse of the absolute value of the other but, as Spitzak points out, that doesn't matter.

Pending further discussion, I now favor "negative".

Peter Brown (talk) 17:38, 15 January 2020 (UTC)

I don't. It is too easily interpreted as "make x negative" (by taking the negation of its absolute value). —David Eppstein (talk) 18:22, 15 January 2020 (UTC)

@David Eppstein:

By "the negation of its absolute value", I assume that you mean −1 times the absolute value. I have argued that this is a nonstandard use of the term "negation", but let's allow that for the moment. The proposed wording is:

In mathematics, it generally indicates a choice of exactly two possible values, one of which is the negative of the other.

You object that "negative" could mean the negation of the absolute value. Suppose that it does. Now consider the formula "√4 = ± 2", which is a pretty standard use of ±. On what you regard as a poor interpretation of ±, this comes to:

The square root of 4 has two values, one of which is the negative of the other.

But this is right, isn't it? √4 does have two values, and one (−2) is the negative (in either sense) of the other (+2). So whether "the negative" means the negation of the given value or the negation of its absolute value, the proposed wording comes out correct.

Peter Brown (talk) 19:35, 15 January 2020 (UTC)

I have presented strong evidence in the form of Google Scholar search results that the whole premise of your claim for "negation" to be incorrect is false. Why are you ignoring this and continuing to repeat this false claim? —David Eppstein (talk) 20:21, 15 January 2020 (UTC)

Not sure what claim you are calling false. You got only 532 hits with "additive inverse" and "floating point" as keywords. Thank you for the effort; that does indicate that "additive inverse" is a bad choice for the context in question, so I have abandoned it in favor of "negative". You dislike that as well, but your argument in this case is far less persuasive — you suggest that the word might be construed as specifying the function f (x) = (-1)|x| rather than f (x) = (-1)x. Perhaps so, but Spitzak and I have both pointed out that this doesn't matter — the definition of ± comes out the same same whichever way you interpret "negative". Peter Brown (talk) 21:54, 15 January 2020 (UTC)

I am calling false your claim that "negation" is erroneous. The search results I cited show it to be in wide use professionally. —David Eppstein (talk) 22:42, 15 January 2020 (UTC)

I can get bigger numbers — 827,000 hits if I use "negation" as my only search key on Google Scholar. Yes, the term is in wide use.

I claimed negation was "erroneous"? Scan the entire talk page; you'll find that your latest post is the very first occurrence of that term.

I and Spitzak prefer "negative" in the article. You object, on the basis that the term is ambiguous, but we have argued that the ambiguity is unimportant. So far, you have not attempted a rebuttal to our argument.

Peter Brown (talk) 00:06, 16 January 2020 (UTC)

You are being disingenuous. If you use "megation" without other context, most of the hits have other meanings. And why do you think scanning this talk page for occurrences will produce meaningful results? —David Eppstein (talk) 00:16, 16 January 2020 (UTC)

Hyphen or endash in title?

Somebody is correcting all the links from plus-minus sign to plus–minus sign. However I question whether the name should be using an endash. Most hypenated words used as titles in Wikipedia seem to use hyphen, for instance anti-social behavior. Should this be renamed back to a hyphen? Spitzak (talk) 02:42, 9 July 2021 (UTC)

An en-dash would make more sense with MOS:ENBETWEEN, as the plus and minus are equal rather than one modifying or being subsidiary to the other. You can find it both ways in the literature, with another variation "plus/minus sign" also popular. —David Eppstein (talk) 05:57, 9 July 2021 (UTC)

In this case, for a Wikipedia page title, I would favour the hyphen/minus sign because it is easier to type on most QWERTY, AZERTY and QWERTZ keyboards. The page happens to be headed with an en dash, however, and I prefer not to change the title of a Wikipedia page without an extremely good reason. At least there exists a redirection from the title with hyphen/minus (which users are bound to try) to the "official" one with en dash.

Ease of typing has no role or effect here; redirects serve, as you note, to take care of that. Dicklyon (talk) 16:11, 14 July 2021 (UTC)

FWIW, the official Unicode name of that character is PLUS-MINUS SIGN with a hyphen/minus. — Tonymec (talk) 09:55, 9 July 2021 (UTC)

Not worth much, since Unicode spells character names using ASCII in general. Dicklyon (talk) 16:11, 14 July 2021 (UTC)

exclusive disjunction for plus-or-minus

Plus-or-minus can be used as INCLUSIVE disjunction or EXCLUSIVE disjunction. The article currently highlights INCLUSIVE disjunction, and only hints at EXCLUSIVE disjunction, in its discussion of the Taylor series for the sine function, but then points out that a more rigorous presentation would eliminate the need for the plus-or-minus symbol.

Here are 2 examples of exclusive disjunction that should be incorporated into the article.

1. If x is any real number, then the square root of x^2 is plus-or-minus x, with 'minus' being chosen if, and only if, x < 0.

2. In Trigonometry, the half-angle formulas are preceded by a plus-or-minus sign. This does not mean that both the positive and negative expressions are valid. Rather, it depends on the quadrant in which the half-angle terminates.

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/07%3A_Trigonometric_Identities_and_Equations/7.03%3A_Double-Angle_Half-Angle_and_Reduction_Formulas Kontribuanto (talk) 22:58, 14 May 2024 (UTC)