Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Occasionally I see the $\mp$ symbol, but I don't really know what it is for, except in conjunction with the $\pm$ symbol thus: $a \pm b \mp c$ which (I believe) means $a+b-c$ or $a-b+c$ (please correct me if I am wrong). Is there any other mathematical usage for the $\mp$ symbol, particularly on its own ?

share|cite|improve this question
It has the same meaning as $\pm$, but as you noted, when used in conjunction, they have "opposite" meanings – M Turgeon May 30 '12 at 13:57
Sometimes it is used to indicate alternating signs in a series, starting with a minus, as in $x-\frac{x^3}{3!}+\frac{x^5}{5!} \mp \ldots$ – marlu May 30 '12 at 14:01
I upvoted @marlu's comment, but then I got worried that it was not actually correct. The example is a little bit wrong, and when I tried to fix it I was not aple to support the point I thought was being made. All I could come up with were things like ${(x\pm y)}^n = x^n \pm x^{n-1}y + x^{n-2}y^2 \pm \cdots $ where there is already a $\pm$ outside to refer to. – MJD May 30 '12 at 15:18
up vote 18 down vote accepted

$\mp$ really only has a use when written in the same expressions as $\pm$.

The one that comes to mind is $\cos (\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta$.

But I suppose if you really wanted to, you could write things like $\sin(\alpha \mp \beta) = \sin \alpha \cos \beta \mp \cos \alpha \sin \beta$... if you really wanted to.

On a more humorous vein, it wouldn't surprise me if someone overloaded the symbol to have a different meaning too. Most likely someone like Conway (as in, Combinatorial Game Theory Conway, not Complex Analysis Conway), who thought $+_n$ was a perfectly good name for a state of a game (not an operation).

an aside

On a non-mathematical note, $\pm$ denotes an advantageous position for white in chess. $\mp$ denotes a position for black.

If we really go for it, $\mp$ looks like (干) wiki page, which means 'to dry' in Japanese and might mean 'to do' in Mandarin. $\pm$ looks like (士)wiki page, which might mean 'gentleman' in Japanese and is used in the symbols for doctorate and doctor's thesis.

share|cite|improve this answer
Thank you, that is helpful. @marlu wrote in a comment to my OP that "Sometimes it is used to indicate alternating signs in a series, starting with a minus, as in $x-\frac{x^3}{3!}+\frac{x^5}{5!} \mp \ldots$" - is that not standard usage ? – Joe King May 30 '12 at 14:38
I am a high-level chess player and have read dozens of chess books, and I have never once seen the notation $\pm$ or $\mp$ used in chess. Everywhere I have ever read, an advantage for white is written +/-, while an advantage for black is written -/+. – BlueRaja - Danny Pflughoeft May 30 '12 at 16:13
@BlueRaja-DannyPflughoeft: I've been an amateur chess player, I've read quite many books (with descriptive notation instead of algebraic!) and I'm pretty sure (not totally) of having seen $\pm$ and $\mp$ – leonbloy May 30 '12 at 16:16
@leon: Wikipedia seems to back that. Perhaps we are just reading different books :) (then again, wikipedia also makes a distinction between +/- and +-, a distinction I doubt is in wide use) – BlueRaja - Danny Pflughoeft May 30 '12 at 16:17
@BlueRaja-DannyPflughoeft : it is somewhat surprising that a high-level chess player is unfamiliar with the Chess Informant notation (or am I a bit too old? :) ). In CI $\pm$ ($\mp$) stands for "White (Black) stands clearly better", whereas $+-$ ($-+$) stands for "White (Black) has a decisive advantage" – Andrea Mori Aug 28 '12 at 22:02

You are correct; $\mp$ only makes sense in a formula that already has $\pm$.

One simple and useful example is that when $x$ is small, ${1\over{1\pm x}}\approx 1\mp x$.

share|cite|improve this answer
Also $x^3 \pm y^3 = (x\pm y)(x^2 \mp xy + y^2)$ – Dilip Sarwate May 30 '12 at 14:34

Like the other answerer, I've only seen it used in the same line as a $\pm$, to mean "positive when the other term is negative and negative when the other term is positive." So, for instance, if we were to say

$\pm a = \mp b$

that would imply that

$ a = -b $


$ -a = b $

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.