# List of mathematical abbreviations

This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology.

*This list is limited to abbreviations of two or more letters (excluding number sets). The capitalization of some of these abbreviations is not standardized – different authors might use different capitalizations.*

- A – adele ring or algebraic numbers.
- AC – Axiom of Choice,
^{[1]}or set of absolutely continuous functions. - a.c. – absolutely continuous.
- acrd – inverse chord function.
- ad – adjoint representation (or adjoint action) of a Lie group.
- 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*.*) - arcexc – inverse excosecant function. (
*Also written as*arcexcsc*,*arcexcosec*.*) - arcexcosec – inverse excosecant function. (
*Also written as*arcexcsc*,*arcexc*.*) - arcexcsc – inverse excosecant function. (
*Also written as*arcexcosec*,*arcexc*.*) - arcexs – inverse exsecant function. (
*Also written as*arcexsec*.*) - arcexsec – inverse exsecant function. (
*Also written as*arcexs*.*) - 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.
- arctan2 – inverse tangent function with two arguments. (
*Also written as*atan2*.*) - arg – argument of.
^{[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.
- atan2 – inverse tangent function with two arguments. (
*Also written as*arctan2*.*) - A.P. – arithmetic progression.
- Aut – automorphism group.
- bd – boundary. (
*Also written as*fr*or*∂*.*) - Bi – Airy function of the second kind.
- BIDMAS – Brackets, Indices, Divide, Multiply, Add, Subtract.
^{[3]} - Bias – bias of an estimator .
- BWOC – by way of contradiction.
- C – complex numbers.
- Card – cardinality of a set.
^{[4]}(Card(*X*)*is also written*#*X*, ♯*X**or*|*X*|*.*) - cas – cos + sin function.
- cdf – cumulative distribution function.
- c.f. – cumulative frequency.
- c.c. – complex conjugate.
- char – characteristic of a ring.
- Chi – hyperbolic cosine integral function.
- Ci – cosine integral function.
- cis – cos + i sin function. (
*Also written as*expi*.*) - Cl – conjugacy class.
- cl – topological closure.
- CLT – central limit theorem.
- cod, codom – codomain.
- cok, coker – cokernel.
- colsp – column space of a matrix.
- conv – convex hull of a set.
- 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.
- cosiv – coversine function. (
*Also written as*cover*,*covers*,*cvs*.*) - cot – cotangent function. (
*Also written as*ctg*.*) - coth – hyperbolic cotangent function.
- cov – covariance of a pair of random variables.
- cover – coversine function. (
*Also written as*covers*,*cvs*,*cosiv*.*) - covercos – covercosine function. (
*Also written as*cvc*.*) - covers – coversine function. (
*Also written as*cover*,*cvs*,*cosiv*.*) - crd – chord function.
- csc – cosecant function. (
*Also written as*cosec*.*) - csch – hyperbolic cosecant function. (
*Also written as*cosech*.*) - ctg – cotangent function. (
*Also written as*cot*.*) - curl – curl of a vector field. (
*Also written as*rot*.*) - cvc – covercosine function. (
*Also written as*covercos*.*) - cvs – coversine function. (
*Also written as*cover*,*covers*,*cosiv*.*) - def – define or definition.
- deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (
*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.
- DNE – a solution for an expression does not exist, or is undefined. Generally used with limits and integrals.
- dom, domain – domain of a function.
^{[1]}(*Or, more generally, a relation.*) - End – categories of endomorphisms.
- Ei – exponential integral function.
- epi – epigraph of a function.
- Eqn – equation.
- erf – error function.
- erfc – complementary error function.
- erfcx – scaled complementary error function.
- erfi – imaginary error function.
- etr – exponent of the trace.
- exc – excosecant function. (
*Also written as*excsc*,*excosec*.*) - excosec – excosecant function. (
*Also written as*excsc*,*exc*.*) - excsc – excosecant function. (
*Also written as*excosec*,*exc*.*) - exs – exsecant function. (
*Also written as*exsec*.*) - exsec – exsecant function. (
*Also written as*exs*.*) - exp – exponential function. (exp
*x**is also written as**e*)^{x}. - expi – cos + i sin function. (
*Also written as*cis*.*) - expm1 – exponential minus 1 function. (
*Also written as*exp1m*.*) - exp1m – exponential minus 1 function. (
*Also written as*expm1*.*) - Ext – Ext functor.
- ext – exterior.
- extr – a set of extreme points of a set.
- FIP – finite intersection property.
- FOC – first order condition.
- FOL – first-order logic.
- fr – boundary. (
*Also written as*bd*or*∂*.*) - Frob – Frobenius endomorphism.
- Gal – Galois group. (
*Also written as*Γ*.*) - gcd – greatest common divisor of two numbers. (
*Also written as*hcf*.*) - gd – Gudermannian function.
- GF – Galois field.
- GF – generating function.
- GL – general linear group.
- G.M. – geometric mean.
- glb – greatest lower bound. (
*Also written as*inf*.*) - G.P. – geometric progression.
- grad – gradient of a function.
- graph – graph of a function.
- H – quaternion numbers.
- hacover – hacoversine function. (
*Also written as*hacovers*,*hcv*.*) - hacovercos – hacovercosine function. (
*Also written as*hcc*.*) - hacovers – hacoversine function. (
*Also written as*hacover*,*hcv*.*) - hav – haversine function. (
*Also written as*sem*.*) - havercos – havercosine function. (
*Also written as*hvc*.*) - hcc – hacovercosine function. (
*Also written as*hacovercos*.*) - hcv – hacoversine function. (
*Also written as*hacover*,*hacovers*.*) - hcf – highest common factor of two numbers. (
*Also written as*gcd*.*) - H.M. – harmonic mean.
- HOL – higher-order logic.
- Hom – Hom functor.
- hom – hom-class.
- hot – higher order term.
- HOTPO – half or triple plus one.
- hvc – havercosine function. (
*Also written as*havercos*.*) - hyp – hypograph of a function.
- iff – if and only if.
- IH – induction hypothesis.
- iid – independent and identically distributed random variables.
- Im – imaginary part of a complex number.
^{[2]}(*Also written as**.*) - im – image.
- inf – infimum of a set. (
*Also written as*glb*.*) - int – interior.
- I.o. – Infinitely often.
- ker – kernel.
- lb – binary logarithm (log
_{2}). (*Also written as*ld*.*) - lcm – lowest common multiple (a.k.a. least common multiple) of two numbers.
- LCHS – locally compact Hausdorff second countable.
- ld – binary logarithm (log
_{2}). (*Also written as*lb*.*) - lsc – lower semi-continuity.
- 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.
- LLN – law of large numbers.
- ln – natural logarithm, log
_{e}. - lnp1 – natural logarithm plus 1 function.
- ln1p – natural logarithm plus 1 function.
- 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.
- MGF – moment-generating function.
- M.I. – mathematical induction.
- min – minimum of a set.
- mod – modulo.
- Mp – metaplectic group.
- mtanh – modified hyperbolic tangent function. (
*Also written as*mth*.*) - mth – modified hyperbolic tangent function. (
*Also written as*mtanh*.*) - mx – matrix.
- N – natural numbers.
- NAND – not-and in logic.
- No. – number.
- NOR – not-or in logic.
- NTS – need to show.
- Null, null – (
*See Kernel.*) - Nullity, nullity – nullity.
- O – octonion numbers.
- OBGF – ordinary bivariate generating function.
- ob – object class.
- ord – ordinal number of a well-ordered set.
^{[4]} - pdf – probability density function.
- pf – proof.
- PGL – projective general linear group.
- Pin – pin group.
- pmf – probability mass function.
- Pn – previous number.
- Pr – probability of an event. (
*See Probability theory. Also written as*P*or**.*) - probit – probit function.
- PSL – projective special linear group.
- PSO – projective orthogonal group.
- PSU – projective special unitary group.
- PU – projective unitary group.
- Q – rational numbers.
- 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 geometrical construction.
- R – real numbers.
- ran – range of a function.
- rank – rank of a matrix. (
*Also written as*rk*.*) - Re – real part of a complex number.
^{[2]}(*Also written**.*) - resp – respectively.
- RHS – right-hand side of an equation.
- rk – rank. (
*Also written as*rank*.*) - RMS, rms – root mean square.
- rng – non-unital ring.
- rot – rotor of a vector field. (
*Also written as*curl*.*) - rowsp – row space of a matrix.
- RTP – required to prove.
- RV – random variable. (
*Also written as*R.V*.*) - S – sedenion numbers.
- SD – standard deviation.
- SE – standard error.
- sec – secant function.
- sech – hyperbolic secant function.
- seg – initial segment of.
^{[1]} - sem – haversine function. (
*Also written as*hav*.*) - SFIP – strong finite intersection property.
- sgn – sign function.
- Shi – hyperbolic sine integral function.
- Si – sine integral function.
- sigmoid – sigmoid function.
- sin – sine function.
- sinc – sinc function.
- sinh – hyperbolic sine function.
- siv – versine function. (
*Also written as*ver*,*vers*.*) - SL – special linear group.
- SO – special orthogonal group.
- SOC – second order condition.
- Soln – solution.
- Sp – symplectic group.
- Sp – trace of a matrix, from the German "spur" used for the trace.
- sp, span – linear span of a set of vectors. (
*Also**written with angle brackets.*) - Spec – spectrum of a ring.
- Spin – spin group.
- s.t. – such that
*or*so that*or*subject to. - st – standard part function.
- STP – [it is] sufficient to prove.
- SU – special unitary group.
- sup – supremum of a set.
^{[1]}(*Also written as*lub*, which stands for least upper bound.*) - supp – support of a function.
- swish – swish function, an activation function in data analysis.
- Sym – symmetric group (Sym(
*n*)*is also written as*S_{n}) or symmetric algebra. - tan – tangent function. (
*Also written as*tgn*,*tg*.*) - tanh – hyperbolic tangent function.
- TFAE – the following are equivalent.
- tg – tangent function. (
*Also written as*tan*,*tgn*.*) - tgn – tangent function. (
*Also written as*tan*,*tg*.*) - Thm – theorem.
- Tor – Tor functor.
- Tr – field trace.
- tr – trace of a matrix or linear transformation. (
*Also written as*Sp*.*) - undef – a function or expression is undefined.
- usc – upper semi-continuity.
- V – volume.
- var – variance of a random variable.
- vcs – vercosine function. (
*Also written as*vercos*.*) - ver – versine function. (
*Also written as*vers*,*siv*.*) - vercos – vercosine function. (
*Also written as*vcs*.*) - vers – versine function. (
*Also written as*ver*,*siv*.*) - 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]} - WOP – well-ordered principle.
- wp1 – with probability 1.
- wrt – with respect to
*or*with regard to. - WTP – want to prove.
- WTS – want to show.
- XOR – exclusive or in logic.
- Z – integer numbers.
- ZF – Zermelo–Fraenkel axioms of set theory.
^{[4]} - ZFC – Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory.
^{[4]}

## See also[edit]

- Greek letters used in mathematics, science, and engineering
- ISO 31-11
- Language of mathematics
- Mathematical Alphanumeric Symbols Unicode block
- List of mathematical jargon
- Mathematical notation
- Notation in probability and statistics
- Physical constants
- List of mathematical uses of Latin letters
- List of logic symbols
- Glossary of mathematical symbols
- Mathematical operators and symbols in Unicode
- List of mathematical functions

## References[edit]

- ^
^{a}^{b}^{c}^{d}^{e}^{f}Goldrei, Derek (1996).*Classic Set Theory*. London, UK: Chapman and Hall. pp. 283–287 (Index). ISBN 0-412-60610-0. - ^
^{a}^{b}^{c}Priestley, H. A. (2003).*Introduction to Complex Analysis*(2 ed.). Oxford University Press. p. 321 (Notation index). ISBN 978-0-19-852562-2. **^**"How to use BIDMAS to solve equations".*BBC Bitesize*. Retrieved 2020-08-08.- ^
^{a}^{b}^{c}^{d}Hamilton, A. G. (1982).*Numbers, sets and axioms*. Cambridge University Press. pp. 249–251 (Index of symbols). ISBN 0-521-24509-5. **^**Raymond, Eric S. (2003), "LERP",*Jargon File*, 4.4.7**^**Jolley, L.B.W. (1961).*Summation of Series*(2 (revised) ed.). New York, USA: Dover Publications, Inc. LCCN 61-65274.