# List of mathematical abbreviations

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This article is a listing of abbreviated names of mathematical functions, function-like operators and other mathematical terminology.

*This list is limited to abbreviations of two or more letters. The capitalization of some of these abbreviations is not standardized – different authors use different capitalizations.*- {{ safesubst:#invoke:Unsubst||$N=Expand list |date=__DATE__ |$B=
*This list is incomplete; you can help by expanding it*.Template:TDMCA

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- AC – Axiom of Choice.
^{[1]} - a.c. - absolutely continuous.
- adj – adjugate of a matrix.
- a.e. – almost everywhere.
- Ai – Airy function.
- AL - Action limit.
- Alt – alternating group (Alt(
*n*)*is also written as*A_{n}.) - A.M. - arithmetic mean.
- arccos – inverse cosine function.
- arccosec – inverse cosecant function. (
*Also written as*arccsc.) - arccot – inverse cotangent function.
- arccsc – inverse cosecant function. (
*Also written as*arccosec.) - arcosech – inverse hyperbolic cosecant function. (
*Also written as*arcsch.) - arcosh – inverse hyperbolic cosine function.
- arcoth – inverse hyperbolic cotangent function.
- arcsch – inverse hyperbolic cosecant function. (
*Also written as*arcosech.) - arcsec – inverse secant function.
- arcsin – inverse sine function.
- arctan – inverse tangent function.
- arg – argument of a complex number.
^{[2]} - arg max – argument of the maximum.
- arg min – argument of the minimum.
- arsech – inverse hyperbolic secant function.
- arsinh – inverse hyperbolic sine function.
- artanh – inverse hyperbolic tangent function.
- a.s. – almost surely.
- A.P. - arithmetic progression.
- Aut – automorphism group.
- Bi – Airy function of the second kind.
- Card – cardinality of a set.
^{[3]}(Card(*X*)*is also written*#*X*, ♯*X**or*|*X*|.) - cdf – cumulative distribution function.
- c.f. - cumulative frequency.
- char – characteristic of a ring.
- Chi - hyperbolic cosine integral function.
- Ci - cosine integral function.
- cis - cos + i sin function.
- Cl – topological closure.
- cod – codomain. (
*Also written as*codom.) - codom – codomain. (
*Also written as*cod.) - Cor - corollary.
- corr - correlation.
- cos – cosine function.
- cosec – cosecant function. (
*Also written as*csc.) - cosech – hyperbolic cosecant function. (
*Also written as*csch.) - cosh – hyperbolic cosine function.
- cot – cotangent function.
- coth – hyperbolic cotangent function.
- cov – covariance of a pair of random variables.
- csc – cosecant function. (
*Also written as*cosec.) - csch – hyperbolic cosecant function. (
*Also written as*cosech.) - curl – curl of a vector field. (
*Also written as*rot.) - def - define or definition.
- deg – degree of a polynomial. (
*Also written as*∂.) - del – del, a differential operator. (
*Also written as*.) - det – determinant of a matrix or linear transformation.
- dim – dimension of a vector space.
- div – divergence of a vector field.
- dkl – decalitre
- DNE - a solution for an expression does not exist, or is undefined. Generally used with limits and integrals.
- dom – domain of a function.
^{[1]}(*Or, more generally, a relation.*) - End – categories of endomorphisms.
- Ei – exponential integral function.
- Eqn – equation.
- erf – error function.
- erfc – complementary error function.
- exp – exponential function. (exp
*x**is also written as**e*.)^{x} - Ext – Ext functor.
- ext – exterior.
- FOL – first-order logic.
- Frob – Frobenius endomorphism.
- Gal – Galois group. (
*Also written as*Γ.) - gcd – greatest common divisor of two numbers. (
*Also written as*hcf.) - GF - Galois field.
- GL – general linear group.
- G.M. - geometric mean.
- glb – greatest lower bound. (
*Also written as*inf.) - G.P. - geometric progression.
- grad – gradient of a scalar field.
- hcf – highest common factor of two numbers. (
*Also written as*gcd.) - H.M. - harmonic mean.
- HOL – higher-order logic.
- Hom – Hom functor.
- iff – if and only if.
- iid - independent and identically distributed random variables.
- Im –
*either*image of a function^{[4]}*or*imaginary part of a complex number^{[2]}(*which is also written*). - inf – infimum of a set. (
*Also written as*glb.) - int – interior.
- Ker – kernel.
^{[4]} - lcm – lowest common multiple of two numbers.
- lerp – linear interpolation.
^{[5]} - lg – common logarithm (log
_{10})*or*binary logarithm (log_{2}). - LHS – left-hand side of an equation.
- Li – offset logarithmic integral function.
- li – logarithmic integral function
*or*linearly independent. - lim – limit of a sequence, or of a function.
- lim inf – limit inferior.
- lim sup – limit superior.
- ln – natural logarithm, log
_{e}. - log – logarithm. (
*If without a subscript, this may mean either*log_{10}*or*log_{e}.) - logh – natural logarithm, log
_{e}.^{[6]} - LST – language of set theory.
- lub – least upper bound.
^{[1]}(*Also written*sup.) - max – maximum of a set.
- M.I. - mathematical induction.
- min – minimum of a set.
- mod – modulo.
- mx – matrix.
- NAND – not-and in logic.
- No. – number.
- NOR – not-or in logic.
- NTS – need to show.
- ord – ordinal number of a well-ordered set.
^{[3]} - pdf – probability density function.
- pf – proof.
- PGL – projective general linear group.
- pmf – probability mass function.
- Pr – probability of an event. (
*See Probability theory. Also written as*P*or*.) - PSL – projective special linear group.
- QED – "Quod erat demonstrandum", a Latin phrase used at the end of a definitive proof.
- QEF – "quod erat faciendum", a Latin phrase sometimes used at the end of a construction.
- ran – range of a function.
- Re – real part of a complex number.
^{[2]}(*Also written*.) - resp – respectively.
- RHS – right-hand side of an equation.
- Rk – rank.
- RMS - root mean square.(
*Also written as*rms.) - rms - root mean square. (
*Also written as*RMS.) - rng – non-unital ring.
- rot – rotor of a vector field. (
*Also written as*curl.) - RTP – required to prove.
- RV – Random Variable. (or as R.V.)
- sec – secant function.
- sech – hyperbolic secant function.
- seg – initial segment of.
^{[1]} - sgn – signum function.
- Shi - hyperbolic sine integral function.
- Si - sine integral function.
- sin – sine function.
- sinc – sinc function.
- sinh – hyperbolic sine function.
- SL – special linear group.
- Soln – solution.
- Sp – linear span of a set of vectors. (
*Also written with angle brackets.*) - Spec – spectrum of a ring.
- st – such that
*or*so that. - STP – [it is] sufficient to prove.
- sup – supremum of a set.
^{[1]}(*Also written*lub.) - supp – support of a function.
- Sym – symmetric group (Sym(
*n*)*is also written as*S_{n}.) - tan – tangent function.
- tanh – hyperbolic tangent function.
- TFAE – the following are equivalent.
- Thm – theorem.
- Tor – Tor functor.
- Tr – trace, either the field trace, or the trace of a matrix or linear transformation.
- undef - a function or expression is undefined
- var – variance of a random variable.
- W^5 – which was what we wanted. Synonym of Q.E.D.
- walog – without any loss of generality.
- wff – well-formed formula.
- whp - with high probability.
- wlog – without loss of generality.
- WMA - we may assume.
- WO – well-ordered set.
^{[1]} - wrt – with respect to
*or*with regard to. - WTP – want to prove.
- WTS – want to show.
- XOR - exclusive or in logic.
- ZF – Zermelo–Fraenkel axioms of set theory.
^{[3]} - ZFC – Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory.
^{[3]}

## References

- ↑
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- ↑ Jolley, L.B.W. (1961), Summation of Series, Second Revised Edition Dover Publications, INC., New York, Library of Congress: 61-65274

## See also

- Greek letters used in mathematics, science, and engineering
- ISO 31-11
- Mathematical alphanumeric symbols
- Mathematical jargon
- Mathematical notation
- Notation in probability and statistics
- Physical constants
- Roman letters used in mathematics
- Table of logic symbols
- Table of mathematical symbols
- Unicode mathematical operators