Minus or plus (∓) in LaTeX
The minus-or-plus sign, \mp, is the companion of \pm, used when two related terms in the same expression need their signs to alternate in opposite directions.
LaTeX command
\mpNot the symbol you meant? Draw it to find the command →
\mp almost never appears alone; it is used alongside \pm in the same formula so that reading the top signs throughout gives one valid equation, and reading the bottom signs throughout gives another. Trigonometric addition and subtraction identities are the clearest example of this pairing.
Like \pm, the command \mp is a core LaTeX symbol, not part of amsmath, so it works in any document or in KaTeX without loading extra packages. It is typeset as a standard binary operator with automatic spacing.
Outside pure algebra, \mp turns up in physics whenever a formula distinguishes between two related but oppositely signed processes, for example matter and antimatter counterparts, or forward and backward propagating waves.
Examples
$\cos(a\pm b) = \cos a\cos b \mp \sin a\sin b$the cosine addition and subtraction identity, paired with \pm
$e^{\mp i\theta} = \cos\theta \mp i\sin\theta$the two complex exponential identities in one line
$(a \pm b)^2 - (a \mp b)^2 = 4ab$\pm and \mp used together in one identity
Tips and common mistakes
- Read a combined
\pm/\mpformula as two separate equations: take every top sign together for one, every bottom sign together for the other. \mpis not a not-equal or different-from symbol, it strictly means the sign is opposite to a paired\pmelsewhere in the same expression.\mpalmost always appears together with\pmin the same formula; using it in isolation is rare and usually a sign something is missing.- No package is needed,
\mpis a core LaTeX command.
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What does the minus-or-plus symbol mean?
It means the sign is the opposite of a paired \pm elsewhere in the same formula: where \pm reads as plus, the paired \mp reads as minus, and vice versa.
How do you type the minus-or-plus sign in LaTeX?
Use \mp inside maths mode, for example . No package is required.
When do you use \mp instead of \pm?
Use \mp when a formula already contains \pm and needs a second quantity whose sign alternates in the opposite direction, as in trigonometric addition identities.
Is \mp part of amsmath?
No, \mp is defined in core LaTeX, the same as \pm, so it works without loading amsmath.