A pair of curly braces — the workhorse group.
{ $|$ }x^{n+1}Brackets
3 expansionsA pair of round brackets.
( $|$ )f(x + y)A pair of square brackets.
[ $|$ ]\mathbb{E}[X]Set theory
46 expansionsThe empty set — the set containing no elements.
\varnothingA \cap B = \varnothingSet literal: elements listed inside braces.
\{ $|$ \}\{ 1, 2, 3 \}Set-builder notation: elements satisfying a condition.
\{ $|$ \mid \}\{ x \in \mathbb{N} \mid x > 3 \}Union — everything in either set.
\cupA \cup BUnion over a range with lower and upper bound.
\bigcup_{ $|$ }^{ }{ }\bigcup_{i=1}^{n} A_iUnion over an index set.
\bigcup_{ $|$ }{ }\bigcup_{i \in I} A_iIntersection — what both sets share.
\capA \cap BIntersection over a range with lower and upper bound.
\bigcap_{ $|$ }^{ }{ }\bigcap_{i=1}^{n} A_iIntersection over an index set.
\bigcap_{ $|$ }{ }\bigcap_{i \in I} A_iSet difference — in the left set but not the right.
\setminusA \setminus BSymmetric difference — in exactly one of the two sets.
\triangleA \triangle BCartesian product — the set of ordered pairs.
\timesA \times BDisjoint union — a union of sets known to be disjoint.
\dot\cupA \dot\cup BCoproduct / disjoint union in the categorical sense.
\sqcupA \sqcup BComplement as a superscript C, typed after the set.
^\mathrm{ C }A^\mathrm{C}Overbar — complement, closure, or conjugate.
\overline{ $|$ }\overline{A}Power set — the set of all subsets.
\mathcal{ P }( $|$ )\mathcal{P}(A)Subset (often used loosely for ⊆).
\subsetA \subset BProper subset — contained in, but not equal to.
\subsetneqA \subsetneq BSubset or equal — every element of A lies in B.
\subseteqA \subseteq BSuperset (often used loosely for ⊇).
\supsetB \supset AProper superset — contains, but is not equal to.
\supsetneqB \supsetneq ASuperset or equal — B contains every element of A.
\supseteqB \supseteq AMembership — the element belongs to the set.
\inx \in AReverse membership — the set contains the element.
\niA \ni xReverse membership; a readable alias for \ni.
\ownsA \owns xNon-membership.
\notinx \notin AReverse non-membership.
\not\niA \not\ni xBlackboard P — the primes, or a probability measure.
\mathbb{ P }p \in \mathbb{P}The natural numbers.
\mathbb{ N }n \in \mathbb{N}The integers.
\mathbb{ Z }\mathbb{Z} = \{ \ldots, -1, 0, 1, \ldots \}A field, typically a finite field.
\mathbb{ F }\mathbb{F}_qThe rational numbers.
\mathbb{ Q }\mathbb{Q} \subset \mathbb{R}The irrational numbers.
\mathbb{ I }\mathbb{I} = \mathbb{R} \setminus \mathbb{Q}The algebraic numbers.
\mathbb{ A }\mathbb{Q} \subset \mathbb{A}The torus, or the circle group.
\mathbb{ T }\mathbb{T} = \mathbb{R} / \mathbb{Z}The real numbers.
\mathbb{ R }f \colon \mathbb{R} \to \mathbb{R}The real plane.
\mathbb{ R }^2(x, y) \in \mathbb{R}^2Real three-space.
\mathbb{ R }^3v \in \mathbb{R}^3Real n-space, dimension left general.
\mathbb{ R }^nx \in \mathbb{R}^nThe hyperreals of non-standard analysis.
{}^*\mathbb{ R }{}^*\mathbb{R}The complex numbers.
\mathbb{ C }z \in \mathbb{C}The quaternions.
\mathbb{ H }\mathbb{H} \supset \mathbb{C}The octonions.
\mathbb{ O }\mathbb{O} \supset \mathbb{H}A sphere, or the surreal numbers.
\mathbb{ S }\mathbb{S}^2A generic base field, usually ℝ or ℂ.
\mathbb{ K }V \text{ over } \mathbb{K}Logic
24 expansionsUniversal quantifier — holds for every element.
\forall\forall x \in \mathbb{R} \colon x^2 \geq 0Existential quantifier — at least one element works.
\exists\exists n \in \mathbb{N} \colon n > xUnique existence — exactly one element works.
\exists!\exists! x \colon f(x) = 0No such element exists.
\nexists\nexists\, q \in \mathbb{Q} \colon q^2 = 2Logical and — both statements hold.
\landp \land qLogical or — at least one statement holds.
\lorp \lor qLogical negation.
\lnot\lnot pConjunction over a range with bounds.
\bigwedge_{ $|$ }^{ }\bigwedge_{i=1}^{n} p_iConjunction over an index set.
\bigwedge_{ $|$ }\bigwedge_{i \in I} p_iDisjunction over a range with bounds.
\bigvee_{ $|$ }^{ }\bigvee_{i=1}^{n} p_iDisjunction over an index set.
\bigvee_{ $|$ }\bigvee_{i \in I} p_iImplication — a long arrow with proper spacing.
\impliesx > 2 \implies x^2 > 4Reverse implication — the left follows from the right.
\impliedbyx^2 = 4 \impliedby x = 2If and only if — logical equivalence.
\iffx \geq 0 \iff |x| = xSatisfies — the structure is a model of the formula.
\models\mathcal{M} \models \varphiProves — the formula is derivable from the theory.
\vdashT \vdash \varphiReverse turnstile; also left adjoint to.
\dashvF \dashv GVerum — the always-true proposition.
\topp \lor \lnot p \iff \topFalsum — contradiction, the always-false proposition.
\botp \land \lnot p \iff \botTherefore — marks a conclusion.
\therefore\therefore x = 3Because — marks a justification.
\because\because x^2 = 9Upright “s.t.” for use inside a formula.
\text{ s.t. }\exists n \text{ s.t. } n > xUpright “w.l.o.g.” for use inside a formula.
\text{ w.l.o.g. }\text{ w.l.o.g. } a \leq bEnd-of-proof marker.
\blacksquare\blacksquareRelations
23 expansionsNot equal.
\neqa \neq bLess than or equal.
\leqa \leq bGreater than or equal.
\geqa \geq bMuch less than.
\ll\varepsilon \ll 1Much greater than.
\ggn \gg 0Approximately equal.
\approx\pi \approx 3.14159Similar to, or distributed as.
\simX \sim \mathcal{N}(0, 1)Asymptotically or homotopically equivalent.
\simeqa_n \simeq b_nIsomorphic or congruent.
\congG \cong HIdentically equal, or congruent modulo n.
\equiva \equiv b \pmod{n}Proportional to.
\proptoF \propto \frac{1}{r^2}Approaches, or is defined to equal.
\doteqx \doteq yAsymptotically equivalent up to constants.
\asympf(n) \asymp g(n)Definition — the left side is defined by the right.
\coloneqqS \coloneqq \{ 1, 2, 3 \}Precedes in a partial order.
\preca \prec bPrecedes or equals in a partial order.
\preceqa \preceq bSucceeds in a partial order.
\succb \succ aSucceeds or equals in a partial order.
\succeqb \succeq aPerpendicular, or orthogonal.
\perpu \perp vParallel to.
\parallelg \parallel hNot parallel to.
\nparallelg \nparallel hDivides, or the conditioning bar in set-builder notation.
\midd \mid nDoes not divide.
\nmid2 \nmid 7Arrows
19 expansionsMaps to — the standard arrow for a function's type.
\tof \colon X \to YSends an element to its image.
\mapstox \mapsto x^2Rightward arrow.
\rightarrowa \rightarrow bLeftward arrow.
\leftarrowa \leftarrow bTwo-way arrow.
\leftrightarrowa \leftrightarrow bLong rightward arrow, for labelled maps.
\longrightarrowX \longrightarrow YLong leftward arrow.
\longleftarrowX \longleftarrow YDouble arrow — implication in a formula.
\Rightarrowp \Rightarrow qReverse double arrow.
\Leftarrowp \Leftarrow qDouble two-way arrow — equivalence.
\Leftrightarrowp \Leftrightarrow qUpward arrow — increases to, or a limit from below.
\uparrowx_n \uparrow xDownward arrow — decreases to.
\downarrowx_n \downarrow xInjection — an embedding into a larger object.
\hookrightarrow\mathbb{Z} \hookrightarrow \mathbb{Q}Reverse injection arrow.
\hookleftarrow\mathbb{Q} \hookleftarrow \mathbb{Z}Surjection — the map is onto.
\twoheadrightarrowG \twoheadrightarrow G/NSquiggly arrow — rewrites to, or leads to.
\rightsquigarrowx \rightsquigarrow yExtensible arrow with a label above it.
\xrightarrow{ $|$ }a_n \xrightarrow{n \to \infty} aExtensible leftward arrow with a label.
\xleftarrow{ $|$ }X \xleftarrow{f} YExtensible maps-to arrow with a label.
\xmapsto{ $|$ }x \xmapsto{\varphi} ySymbols & spacing
20 expansionsCentred multiplication dot.
\cdota \cdot bComposition of maps, or a ring operation.
\circ(g \circ f)(x)Asterisk operator — convolution, adjoint, or a free slot.
\astf \ast gStar operator — a generic binary operation.
\stara \star bFilled bullet — a placeholder argument.
\bullet\langle \bullet, \bullet \ranglePlus or minus.
\pmx = 2 \pm 0.1Minus or plus — the opposite sign to a nearby ±.
\mpa \pm b \mp cDirect sum, or exclusive or.
\oplusV \oplus WTensor product.
\otimesV \otimes WCircled dot — Hadamard or elementwise product.
\odotA \odot BCentred ellipsis, for use between operators.
\cdotsa_1 + \cdots + a_nBaseline ellipsis, for use between commas.
\ldotsa_1, \ldots, a_nVertical ellipsis, for columns in a matrix.
\vdots\vdotsDiagonal ellipsis, for a matrix diagonal.
\ddots\ddotsDegree sign as a superscript.
^\circ90^\circPrime mark — a derivative or a related object.
^{ \prime }f^{\prime}(x)Colon with function-notation spacing.
\colonf \colon X \to YOne quad of horizontal space.
\quada = b \quad \text{for all } xTwo quads of horizontal space.
\qquada = b \qquad c = dThin space — fine spacing adjustment.
\,\mathbb{R}\,^nGreek & letters
44 expansionsAlpha — angles, coefficients, significance levels.
\alpha\alpha + \beta = \piBeta — a second angle or coefficient.
\beta\beta_1 x + \beta_0Gamma — the gamma function, curves, Euler's constant.
\gamma\gamma \approx 0.5772Delta — a small change, or the Kronecker delta.
\delta\delta_{ij}Epsilon — a small positive quantity (lunate form).
\epsilon\epsilon > 0Varepsilon — the form most analysts prefer.
\varepsilon|x - a| < \varepsilonZeta — the Riemann zeta function.
\zeta\zeta(s) = \sum_{n=1}^{\infty} n^{-s}Eta — efficiency, or a learning rate.
\eta\eta \in (0, 1)Theta — angles and parameter vectors.
\theta\cos \thetaVartheta — the script form of theta.
\vartheta\varthetaIota — an inclusion map.
\iota\iota \colon A \hookrightarrow BKappa — curvature or a condition number.
\kappa\kappa(A)Lambda — eigenvalues, rates, Lebesgue measure.
\lambdaA v = \lambda vMu — a mean, or a measure.
\mu\mu = \mathbb{E}[X]Nu — a second measure, or degrees of freedom.
\nu\nu \ll \muXi — a random variable or auxiliary point.
\xi\xi \in [a, b]Pi — the circle constant, or a projection.
\pi\pi r^2Varpi — the variant form of pi.
\varpi\varpiRho — density, correlation, spectral radius.
\rho\rho(X, Y)Varrho — the variant form of rho.
\varrho\varrhoSigma — standard deviation, or a σ-algebra.
\sigma\sigma^2 = \operatorname{Var}(X)Varsigma — final sigma, used as a variant.
\varsigma\varsigmaTau — time constants, torsion, Kendall's tau.
\tau\tau = 2\piUpsilon.
\upsilon\upsilonPhi — the golden ratio, Euler's totient, angles.
\phi\phi(n)Varphi — the looped form, common for maps.
\varphi\varphi \colon G \to HChi — characters and the chi-squared distribution.
\chi\chi^2Psi — wave functions and digamma.
\psi\psi(x)Omega — frequency, the first infinite ordinal.
\omega\omega = e^{2\pi i / n}Capital gamma — the gamma function, or a contour.
\Gamma\Gamma(n+1) = n!Capital delta — a difference, or the Laplacian.
\Delta\Delta x \to 0Capital theta — tight asymptotic growth.
\Theta\Theta(n \log n)Capital lambda — a diagonal matrix of eigenvalues.
\LambdaA = Q \Lambda Q^{-1}Capital xi.
\Xi\XiCapital pi — a product, or a projection.
\Pi\Pi_{i}Capital sigma — a sum, or a covariance matrix.
\Sigma\Sigma = \operatorname{Cov}(X)Capital upsilon.
\Upsilon\UpsilonCapital phi — the normal CDF, or a map.
\Phi\Phi(z)Capital psi.
\Psi\PsiCapital omega — the sample space, or a domain.
\Omega\omega \in \OmegaScript ell — sequence spaces and lengths.
\ell\ell^2(\mathbb{N})Reduced Planck constant.
\hbar\hbar = \frac{h}{2\pi}Aleph — infinite cardinal numbers.
\aleph\aleph_0Beth — the beth cardinals.
\beth\beth_1 = 2^{\aleph_0}Analysis
38 expansionsInfinity.
\infty\lim_{n \to \infty} a_nLimit with a subscript condition.
\lim_{ $|$ }\lim_{x \to 0} \frac{\sin x}{x} = 1Limit with the arrow already in place.
\lim_{ $|$ \to }\lim_{n \to \infty} \frac{1}{n} = 0Limit superior — the largest accumulation point.
\limsup_{ $|$ }\limsup_{n \to \infty} a_nLimit inferior — the smallest accumulation point.
\liminf_{ $|$ }\liminf_{n \to \infty} a_nSupremum — the least upper bound.
\sup_{ $|$ }\sup_{x \in A} f(x)Infimum — the greatest lower bound.
\inf_{ $|$ }\inf_{x \in A} f(x)Maximum — an attained largest value.
\max\max \{ a, b \}Minimum — an attained smallest value.
\min\min \{ a, b \}The argument at which a maximum is attained.
\operatorname*{ arg\,max }_{ $|$ }\operatorname*{arg\,max}_{x \in A} f(x)The argument at which a minimum is attained.
\operatorname*{ arg\,min }_{ $|$ }\operatorname*{arg\,min}_{\theta} L(\theta)Sum with lower and upper bounds.
\sum_{ $|$ }^{ }\sum_{i=1}^{n} a_iSum over an index set.
\sum_{ $|$ }\sum_{i \in I} a_iInfinite series — the upper bound is already ∞.
\sum_{ $|$ }^{ \infty }\sum_{n=0}^{\infty} \frac{1}{n!} = eProduct with lower and upper bounds.
\prod_{ $|$ }^{ }\prod_{i=1}^{n} a_iProduct over an index set.
\prod_{ $|$ }\prod_{p \in \mathbb{P}} pDefinite integral with both limits.
\int_{ $|$ }^{ }\int_{0}^{1} x^2 \, \mathrm{d}xIntegral over a domain rather than an interval.
\int_{ $|$ }\int_{\Omega} f \, \mathrm{d}\muContour integral around a closed curve.
\oint_{ $|$ }\oint_{\gamma} f(z) \, \mathrm{d}zDouble integral over a region.
\iint_{ $|$ }\iint_{D} f(x, y) \, \mathrm{d}ATriple integral over a volume.
\iiint_{ $|$ }\iiint_{V} \rho \, \mathrm{d}VUpright differential d with its thin space.
\, \mathrm{ d }\int f(x) \, \mathrm{d}xOrdinary derivative as a fraction.
\frac{ \mathrm{ d } $|$ }{ \mathrm{ d } }\frac{\mathrm{d}y}{\mathrm{d}x}Partial derivative as a fraction.
\frac{ \partial $|$ }{ \partial }\frac{\partial f}{\partial x}Partial derivative symbol, also a boundary.
\partial\partial \OmegaNabla — gradient, divergence, or curl.
\nabla\nabla fFraction with numerator and denominator.
\frac{ $|$ }{ }\frac{a}{b}Square root.
\sqrt{ $|$ }\sqrt{x^2 + y^2}nth root — the index goes in the brackets.
\sqrt[ $|$ ]{ }\sqrt[3]{x}Binomial coefficient.
\binom{ $|$ }{ }\binom{n}{k}Exponential function with parentheses ready.
\exp( $|$ )\exp(x + y)Natural logarithm.
\ln\ln e = 1Logarithm with a subscript base.
\log_{ $|$ }\log_{2} nSine.
\sin\sin^2 x + \cos^2 x = 1Cosine.
\cos\cos(2x)Tangent.
\tan\tan x = \frac{\sin x}{\cos x}Big-O — an asymptotic upper bound.
\mathcal{ O }( $|$ )\mathcal{O}(n \log n)Little-o — strictly smaller asymptotic growth.
\mathrm{ o }( $|$ )\mathrm{o}(n)Linear algebra
14 expansionsDeterminant.
\det\det(A) \neq 0Trace — the sum of the diagonal entries.
\operatorname{ tr }\operatorname{tr}(A) = \sum_i a_{ii}Rank — the dimension of the image.
\operatorname{ rank }\operatorname{rank}(A) = nDimension of a vector space.
\dim\dim V = nSpan — all linear combinations of the given vectors.
\operatorname{ span }( $|$ )\operatorname{span}(v_1, v_2)Kernel — the vectors sent to zero.
\ker\ker(f) = \{ 0 \}Image — the set of values actually attained.
\operatorname{ im }\operatorname{im}(f) \subseteq WDiagonal matrix built from the listed entries.
\operatorname{ diag }( $|$ )\operatorname{diag}(\lambda_1, \lambda_2)Projection onto a subspace.
\operatorname{ proj }_{ $|$ }\operatorname{proj}_{U}(v)Identity map or identity matrix.
\mathrm{ id }f \circ f^{-1} = \mathrm{id}Transpose, as an upright sans-serif superscript T.
^\mathsf{ T }A^\mathsf{T} AInverse as a −1 superscript.
^{ -1 }A^{-1} A = IDagger — conjugate transpose or adjoint.
^\daggerA^\daggerInner product of two vectors.
\langle $|$ , \rangle\langle u, v \rangle = 0Algebra
19 expansionsThe set of homomorphisms between two objects.
\operatorname{ Hom }( $|$ , )\operatorname{Hom}(V, W)Endomorphisms — homomorphisms of an object to itself.
\operatorname{ End }( $|$ )\operatorname{End}(V)The automorphism group.
\operatorname{ Aut }( $|$ )\operatorname{Aut}(G)General linear group — invertible matrices.
\operatorname{ GL }_{ $|$ }( )\operatorname{GL}_{n}(\mathbb{R})Special linear group — determinant one.
\operatorname{ SL }_{ $|$ }( )\operatorname{SL}_{2}(\mathbb{Z})Symmetric group on n letters.
\mathfrak{ S }_{ $|$ }\mathfrak{S}_{n}Normal subgroup, or a two-sided ideal.
\trianglelefteqN \trianglelefteq GSemidirect product, normal factor on the left.
\rtimesN \rtimes HSemidirect product, normal factor on the right.
\ltimesH \ltimes NThe integers modulo n.
\mathbb{ Z } / $|$ \mathbb{ Z }\mathbb{Z} / n \mathbb{Z}Binary mod operator inside an expression.
\bmoda \bmod nParenthesised modulus after a congruence.
\pmod{ $|$ }a \equiv b \pmod{n}Unit group, written as a × superscript.
^\timesR^\timesIsomorphism arrow with a tilde above it.
\xrightarrow{ \sim }V \xrightarrow{\sim} WOrder of a group element.
\operatorname{ ord }( $|$ )\operatorname{ord}(g) = 6Characteristic of a ring or field.
\operatorname{ char }( $|$ )\operatorname{char}(\mathbb{F}_p) = pDegree of a polynomial or field extension.
\deg\deg f = 3Greatest common divisor.
\gcd\gcd(a, b) = 1Least common multiple.
\operatorname{ lcm }\operatorname{lcm}(4, 6) = 12Probability
16 expansionsProbability of an event.
\mathbb{ P }( $|$ )\mathbb{P}(A \cup B)Conditional probability, bar already in place.
\mathbb{ P }( $|$ \mid )\mathbb{P}(A \mid B)Expected value.
\mathbb{ E }[ $|$ ]\mathbb{E}[X]Conditional expectation.
\mathbb{ E }[ $|$ \mid ]\mathbb{E}[X \mid \mathcal{F}]Variance.
\operatorname{ Var }( $|$ )\operatorname{Var}(X) = \sigma^2Covariance of two random variables.
\operatorname{ Cov }( $|$ , )\operatorname{Cov}(X, Y)Normal distribution with mean and variance.
\mathcal{ N }( $|$ , )X \sim \mathcal{N}(\mu, \sigma^2)Borel σ-algebra on a space.
\mathcal{ B }( $|$ )\mathcal{B}(\mathbb{R})A σ-algebra of events.
\mathcal{ F }A \in \mathcal{F}A complete probability space triple.
( \Omega, \mathcal{ F }, \mathbb{ P } )( \Omega, \mathcal{F}, \mathbb{P} )Independent and identically distributed.
\overset{ \text{i.i.d.} }{ \sim }X_i \overset{\text{i.i.d.}}{\sim} FIndependent of.
\perp\!\!\!\perpX \perp\!\!\!\perp YAlmost surely — with probability one.
\text{ a.s. }X_n \to X \text{ a.s. }Convergence in distribution.
\xrightarrow{ d }X_n \xrightarrow{d} XConvergence in probability.
\xrightarrow{ \mathbb{ P } }X_n \xrightarrow{\mathbb{P}} XAlmost sure convergence.
\xrightarrow{ \text{a.s.} }X_n \xrightarrow{\text{a.s.}} XAccents & fonts
24 expansionsHat — an estimator or a unit vector.
\hat{ $|$ }\hat{\theta}Wide hat, for expressions longer than one symbol.
\widehat{ $|$ }\widehat{ABC}Bar — a mean, closure, or conjugate.
\bar{ $|$ }\bar{x} = \frac{1}{n} \sum_i x_iTilde — a modified version of an object.
\tilde{ $|$ }\tilde{f}Wide tilde, for longer expressions.
\widetilde{ $|$ }\widetilde{XYZ}Vector arrow.
\vec{ $|$ }\vec{v} \cdot \vec{w}Single dot — the first time derivative.
\dot{ $|$ }\dot{x}(t)Double dot — the second time derivative.
\ddot{ $|$ }\ddot{x} = -\omega^2 xUnderline.
\underline{ $|$ }\underline{a}Brace below an expression with a label under it.
\underbrace{ $|$ }_{ }\underbrace{a + \cdots + a}_{n \text{ times}}Brace above an expression with a label over it.
\overbrace{ $|$ }^{ }\overbrace{x + y}^{s}Places the first argument above the second.
\overset{ $|$ }{ }\overset{!}{=}Places the first argument below the second.
\underset{ $|$ }{ }\underset{n \to \infty}{\lim}Subscript group.
_{ $|$ }a_{ij}Superscript group — powers and indices.
^{ $|$ }x^{n+1}Upright prose inside a formula.
\text{ $|$ }x > 0 \text{ for all } xUpright roman — units and multi-letter names.
\mathrm{ $|$ }\mathrm{d}xBold — vectors and matrices.
\mathbf{ $|$ }\mathbf{A} \mathbf{x}Math italic.
\mathit{ $|$ }\mathit{diff}Sans-serif — categories, or the transpose T.
\mathsf{ $|$ }\mathsf{Set}Monospace.
\mathtt{ $|$ }\mathtt{code}Calligraphic — σ-algebras, categories, Landau O.
\mathcal{ $|$ }\mathcal{F}Fraktur — Lie algebras, ideals, prime ideals.
\mathfrak{ $|$ }\mathfrak{g}Blackboard bold, for any letter not in the list above.
\mathbb{ $|$ }\mathbb{X}Delimiters
13 expansionsAbsolute value, using proper vertical delimiters.
\lvert $|$ \rvert\lvert x - y \rvertNorm of a vector or function.
\lVert $|$ \rVert\lVert x \rVert_2Floor — round down to an integer.
\lfloor $|$ \rfloor\lfloor 3.7 \rfloor = 3Ceiling — round up to an integer.
\lceil $|$ \rceil\lceil 3.2 \rceil = 4Angle brackets — a generated object or a bra-ket.
\langle $|$ \rangle\langle g \rangleAuto-sized parentheses.
\left( $|$ \right)\left( \frac{a}{b} \right)Auto-sized braces.
\left\{ $|$ \right\}\left\{ \frac{a}{b} \right\}Auto-sized square brackets.
\left[ $|$ \right]\left[ \frac{a}{b} \right]Auto-sized absolute value bars.
\left\lvert $|$ \right\rvert\left\lvert \frac{a}{b} \right\rvertAuto-sized norm bars.
\left\lVert $|$ \right\rVert\left\lVert \frac{a}{b} \right\rVertAuto-sized angle brackets.
\left\langle $|$ \right\rangle\left\langle \frac{a}{b} \right\rangleA divider that grows with its surrounding delimiters.
\middle|\left\{ x \middle| \frac{x}{2} \in \mathbb{Z} \right\}Evaluation bar, for substituting a bound.
\left. $|$ \right|_{ }\left. F(x) \right|_{0}^{1}Environments
12 expansionsA single numbered display equation.
\begin{equation}
$|$
\end{equation}\begin{equation}
E = mc^2
\end{equation}Multi-line equations aligned at the & marks, numbered.
\begin{align}
$|$
\end{align}\begin{align}
(a+b)^2 &= a^2 + 2ab + b^2 \\
&= a^2 + b^2 + 2ab
\end{align}The same alignment, without equation numbers.
\begin{align*}
$|$
\end{align*}\begin{align*}
f(x) &= x^2 \\
f'(x) &= 2x
\end{align*}Several centred equations, each on its own line.
\begin{gather}
$|$
\end{gather}\begin{gather}
a = b \\
c = d
\end{gather}A case distinction with conditions on the right.
\begin{cases}
$|$ & \text{if } \\
& \text{else}
\end{cases}\begin{cases}
x & \text{if } x \geq 0 \\
-x & \text{else}
\end{cases}A matrix body with no delimiters.
\begin{matrix}
$|$
\end{matrix}\begin{matrix}
a & b \\
c & d
\end{matrix}Matrix in round brackets — the usual choice.
\begin{pmatrix}
$|$
\end{pmatrix}\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}Matrix in square brackets.
\begin{bmatrix}
$|$
\end{bmatrix}\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}Single bars — a determinant.
\begin{vmatrix}
$|$
\end{vmatrix}\begin{vmatrix}
a & b \\
c & d
\end{vmatrix}Double bars — an operator norm.
\begin{Vmatrix}
$|$
\end{Vmatrix}\begin{Vmatrix}
a & b \\
c & d
\end{Vmatrix}A tiny matrix that fits inside a line of text.
\begin{smallmatrix} $|$ \end{smallmatrix}\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}A general table, with a column specification.
\begin{array}{ $|$ }
\end{array}\begin{array}{cc}
a & b \\
c & d
\end{array}Nothing matches that. Try a symbol name, a LaTeX command, or a word from a description.