# Symbols:LaTeX Commands/ProofWiki Specific

## $\LaTeX$ Commands
This page contains $\LaTeX$ commands which are specific to $\mathsf{Pr} \infty \mathsf{fWiki}$.
 $\AA$ $\quad:\quad$\AA $\qquad$that is: \mathcal A $\Add$ $\quad:\quad$\Add $\qquad$Addition as a Primitive Recursive Function‎ $\adj {\mathbf A}$ $\quad:\quad$\adj {\mathbf A} $\qquad$Adjugate Matrix $\map \Ai {x}$ $\quad:\quad$\map \Ai {x} $\qquad$Airy Function of the First Kind $\am z$ $\quad:\quad$\am z $\qquad$Amplitude $\arccot$ $\quad:\quad$\arccot $\qquad$Arccotangent $\arccsc$ $\quad:\quad$\arccsc $\qquad$Arccosecant $\arcosh$ $\quad:\quad$\arcosh $\qquad$Area Hyperbolic Cosine $\Arcosh$ $\quad:\quad$\Arcosh $\qquad$Complex Area Hyperbolic Cosine $\arcoth$ $\quad:\quad$\arcoth $\qquad$Area Hyperbolic Cotangent $\Arcoth$ $\quad:\quad$\Arcoth $\qquad$Complex Area Hyperbolic Cotangent $\arcsch$ $\quad:\quad$\arcsch $\qquad$Area Hyperbolic Cosecant $\Arcsch$ $\quad:\quad$\Arcsch $\qquad$Complex Area Hyperbolic Cosecant $\arcsec$ $\quad:\quad$\arcsec $\qquad$Arcsecant $\arsech$ $\quad:\quad$\arsech $\qquad$Area Hyperbolic Secant $\Arsech$ $\quad:\quad$\Arsech $\qquad$Complex Area Hyperbolic Secant $\arsinh$ $\quad:\quad$\arsinh $\qquad$Area Hyperbolic Sine $\Arsinh$ $\quad:\quad$\Arsinh $\qquad$Complex Area Hyperbolic Sine $\artanh$ $\quad:\quad$\artanh $\qquad$Area Hyperbolic Tangent $\Artanh$ $\quad:\quad$\Artanh $\qquad$Complex Area Hyperbolic Tangent $\Area$ $\quad:\quad$\Area $\qquad$Area of Plane Figure $\Arg z$ $\quad:\quad$\Arg z $\qquad$Principal Argument of Complex Number $\Aut {S}$ $\quad:\quad$\Aut {S} $\qquad$Automorphism Group $\BB$ $\quad:\quad$\BB $\qquad$that is: \mathcal B $\Bei$ $\quad:\quad$\Bei $\qquad$Bei Function $\Ber$ $\quad:\quad$\Ber $\qquad$Ber Function $\Bernoulli {p}$ $\quad:\quad$\Bernoulli {p} $\qquad$Bernoulli Distribution $\BetaDist {\alpha} {\beta}$ $\quad:\quad$\BetaDist {\alpha} {\beta} $\qquad$Beta Distribution $\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a}$ $\quad:\quad$\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a} $\qquad$Limits of Integration $\bigsize {x}$ $\quad:\quad$\bigsize {x} $\qquad$Absolute Value $\bigvalueat {\delta x} {x \mathop = x_j}$ $\quad:\quad$\bigvalueat {\delta x} {x \mathop = x_j}  $\Binomial {n} {p}$ $\quad:\quad$\Binomial {n} {p} $\qquad$Binomial Distribution $\braket {a} {b}$ $\quad:\quad$\braket {a} {b} $\qquad$Dirac Notation $\bsalpha$ $\quad:\quad$\bsalpha $\bsbeta$ $\quad:\quad$\bsbeta $\bschi$ $\quad:\quad$\bschi $\bsDelta$ $\quad:\quad$\bsDelta $\qquad$a vector '$\Delta$' $\bsdelta$ $\quad:\quad$\bsdelta $\bsepsilon$ $\quad:\quad$\bsepsilon $\bseta$ $\quad:\quad$\bseta $\bsgamma$ $\quad:\quad$\bsgamma $\bsiota$ $\quad:\quad$\bsiota $\bskappa$ $\quad:\quad$\bskappa $\bslambda$ $\quad:\quad$\bslambda $\bsmu$ $\quad:\quad$\bsmu $\bsnu$ $\quad:\quad$\bsnu $\bsomega$ $\quad:\quad$\bsomega $\bsomicron$ $\quad:\quad$\bsomicron $\bsone$ $\quad:\quad$\bsone $\qquad$vector of ones $\bsphi$ $\quad:\quad$\bsphi $\bspi$ $\quad:\quad$\bspi $\bspsi$ $\quad:\quad$\bspsi $\bsrho$ $\quad:\quad$\bsrho $\bssigma$ $\quad:\quad$\bssigma $\bst$ $\quad:\quad$\bst $\qquad$a vector 't' $\bstau$ $\quad:\quad$\bstau $\bstheta$ $\quad:\quad$\bstheta $\bsupsilon$ $\quad:\quad$\bsupsilon $\bsv$ $\quad:\quad$\bsv $\qquad$a vector 'v' $\bsw$ $\quad:\quad$\bsw $\qquad$a vector 'w' $\bsx$ $\quad:\quad$\bsx $\qquad$a vector 'x' $\bsxi$ $\quad:\quad$\bsxi $\bsy$ $\quad:\quad$\bsy $\qquad$a vector 'y' $\bsz$ $\quad:\quad$\bsz $\qquad$a vector 'z' $\bszero$ $\quad:\quad$\bszero $\qquad$vector of zeros $\bszeta$ $\quad:\quad$\bszeta $\map \Card {S}$ $\quad:\quad$\map \Card {S} $\qquad$Cardinality $\card {S}$ $\quad:\quad$\card {S} $\qquad$Cardinality $\Cauchy {x_0} {\gamma}$ $\quad:\quad$\Cauchy {x_0} {\gamma} $\qquad$Cauchy Distribution $\CC$ $\quad:\quad$\CC $\qquad$that is: \mathcal C $\Cdm {f}$ $\quad:\quad$\Cdm {f} $\qquad$Codomain of Mapping $\ceiling {11.98}$ $\quad:\quad$\ceiling {11.98} $\qquad$Ceiling Function $30 \cels$ $\quad:\quad$30 \cels $\qquad$Degrees Celsius $15 \cents$ $\quad:\quad$15 \cents $\qquad$Cent $\Char {R}$ $\quad:\quad$\Char {R} $\qquad$Characteristic of Ring, etc. $\Ci$ $\quad:\quad$\Ci $\qquad$Cosine Integral Function $\cis \theta$ $\quad:\quad$\cis \theta $\qquad$$\cos \theta + i \sin \theta $\cl {S}$ \quad:\quad\cl {S} \qquadClosure (Topology) $\closedint {a} {b}$ \quad:\quad\closedint {a} {b} \qquadClosed Interval $\cmod {z^2}$ \quad:\quad\cmod {z^2} \qquadComplex Modulus $\cn u$ \quad:\quad\cn u \qquadElliptic Function $\condprob {A} {B}$ \quad:\quad\condprob {A} {B} \qquadConditional Probability $\conjclass {x}$ \quad:\quad\conjclass {x} \qquadConjugacy Class $\cont {f}$ \quad:\quad\cont {f} \qquadContent of Polynomial $\ContinuousUniform {a} {b}$ \quad:\quad\ContinuousUniform {a} {b} \qquadContinuous Uniform Distribution $\cosec$ \quad:\quad\cosec \qquadCosecant (alternative form) $\Cosh$ \quad:\quad\Cosh \qquadHyperbolic Cosine $\Coth$ \quad:\quad\Coth \qquadHyperbolic Cotangent $\cov {X, Y}$ \quad:\quad\cov {X, Y} \qquadCovariance $\csch$ \quad:\quad\csch \qquadHyperbolic Cosecant $\Csch$ \quad:\quad\Csch \qquadHyperbolic Cosecant $\curl$ \quad:\quad\curl \qquadCurl Operator $\DD$ \quad:\quad\DD \qquadthat is: \mathcal D $\dfrac {\d x} {\d y}$ \quad:\quad\dfrac {\d x} {\d y} \qquadRoman \d for Derivatives $30 \degrees$ \quad:\quad30 \degrees \qquadDegrees of Angle $\diam$ \quad:\quad\diam \qquadDiameter $\Dic n$ \quad:\quad\Dic n \qquadDicyclic Group $\DiscreteUniform {n}$ \quad:\quad\DiscreteUniform {n} \qquadDiscrete Uniform Distribution $a \divides b$ \quad:\quada \divides b \qquadDivisibility $\dn u$ \quad:\quad\dn u \qquadElliptic Function $\Dom {f}$ \quad:\quad\Dom {f} \qquadDomain of Mapping $\dr {a}$ \quad:\quad\dr {a} \qquadDigital Root $\E$ \quad:\quad\E \qquadElementary Charge $\EE$ \quad:\quad\EE \qquadthat is: \mathcal E $\Ei$ \quad:\quad\Ei \qquadExponential Integral Function $\empty$ \quad:\quad\empty \qquadEmpty Set $\eqclass {x} {\RR}$ \quad:\quad\eqclass {x} {\RR} \qquadEquivalence Class $\erf$ \quad:\quad\erf \qquadError Function $\erfc$ \quad:\quad\erfc \qquadComplementary Error Function $\expect {X}$ \quad:\quad\expect {X} \qquadExpectation $\Exponential {\beta}$ \quad:\quad\Exponential {\beta} \qquadExponential Distribution $\Ext {\gamma}$ \quad:\quad\Ext {\gamma} \qquadExterior $\F$ \quad:\quad\F \qquadFalse $30 \fahr$ \quad:\quad30 \fahr \qquadDegrees Fahrenheit $\family {S_i}$ \quad:\quad\family {S_i} \qquadIndexed Family $\FF$ \quad:\quad\FF \qquadthat is: \mathcal F $\Field {\RR}$ \quad:\quad\Field {\RR} \quadAMSsymbols\quadCustom \mathsf{Pr} \infty \mathsf{fWiki} $\Fix {\pi}$ \quad:\quad\Fix {\pi} \qquadSet of Fixed Elements $\floor {11.98}$ \quad:\quad\floor {11.98} \qquadFloor Function $\fractpart {x}$ \quad:\quad\fractpart {x} \qquadFractional Part $\Frob {R}$ \quad:\quad\Frob {R} \qquadFrobenius Endomorphism $\Gal {S}$ \quad:\quad\Gal {S} \qquadGalois Group $\Gaussian {\mu} {\sigma^2}$ \quad:\quad\Gaussian {\mu} {\sigma^2} \qquadGaussian Distribution $\gen {S}$ \quad:\quad\gen {S} \qquadGenerator $\Geometric {p}$ \quad:\quad\Geometric {p} \qquadGeometric Distribution $\GF$ \quad:\quad\GF \qquadGalois Field $\GG$ \quad:\quad\GG \qquadthat is: \mathcal G $\GL {n, \R}$ \quad:\quad\GL {n, \R} \qquadGeneral Linear Group $\grad {p}$ \quad:\quad\grad {p} \qquadGradient $\harm {r} {z}$ \quad:\quad\harm {r} {z} \qquadGeneral Harmonic Numbers $\hav \theta$ \quad:\quad\hav \theta \qquadHaversine $\hcf$ \quad:\quad\hcf \qquadHighest Common Factor $\H$ \quad:\quad\H \qquadSet of Quaternions $\HH$ \quad:\quad\HH \qquadHilbert Space $\hointl {a} {b}$ \quad:\quad\hointl {a} {b} \qquadLeft Half-Open Interval $\hointr {a} {b}$ \quad:\quad\hointr {a} {b} \qquadRight Half-Open Interval $\horectl a b$ \quad:\quad\horectl a b \qquadHalf-Open Rectangle (on the left) $\horectr c d$ \quad:\quad\horectr c d \qquadHalf-Open Rectangle (on the right) $\ideal {a}$ \quad:\quad\ideal {a} \qquadIdeal of Ring $\II$ \quad:\quad\II \qquadthat is: \mathcal I $\map \Im z$ \quad:\quad\map \Im z \qquadImaginary Part $\Img {f}$ \quad:\quad\Img {f} \qquadImage of Mapping $\index {G} {H}$ \quad:\quad\index {G} {H} \qquadIndex of Subgroup $\inj$ \quad:\quad\inj \qquadCanonical Injection $\Inn {S}$ \quad:\quad\Inn {S} \qquadGroup of Inner Automorphisms $\innerprod {x} {y}$ \quad:\quad\innerprod {x} {y} \qquadInner Product $\Int {\gamma}$ \quad:\quad\Int {\gamma} \qquadInterior $\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a}$ \quad:\quad\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a} \qquadLimits of Integration $\invlaptrans {F}$ \quad:\quad\invlaptrans {F} \qquadInverse Laplace Transform $\JJ$ \quad:\quad\JJ \qquadthat is: \mathcal J $\Kei$ \quad:\quad\Kei \qquadKei Function $\Ker$ \quad:\quad\Ker \qquadKer Function $\KK$ \quad:\quad\KK \qquadthat is: \mathcal K $\laptrans {f}$ \quad:\quad\laptrans {f} \qquadLaplace Transform $\lcm \set {x, y, z}$ \quad:\quad\lcm \set {x, y, z} \qquadLowest Common Multiple $\leadstoandfrom$ \quad:\quad\leadstoandfrom $\leftset {a, b, c}$ \quad:\quad\leftset {a, b, c} \qquadConventional set notation (left only) $\leftparen {a + b + c}$ \quad:\quad\leftparen {a + b + c} \qquadParenthesis (left only) $\len {AB}$ \quad:\quad\len {AB} \qquadLength Function: various $\Li$ \quad:\quad\Li \qquadEulerian Logarithmic Integral $\li$ \quad:\quad\li \qquadLogarithmic Integral $\LL$ \quad:\quad\LL \qquadthat is: \mathcal L $\Ln$ \quad:\quad\Ln \qquadPrincipal Branch of Complex Natural Logarithm $\Log$ \quad:\quad\Log \qquadPrincipal Branch of Complex Natural Logarithm $\map {f} {x}$ \quad:\quad\map {f} {x} \qquadMapping or Function $\meta {metasymbol}$ \quad:\quad\meta {metasymbol} \qquadMetasymbol $27 \minutes$ \quad:\quad27 \minutes \qquadMinutes of Angle or Minutes of Time $\MM$ \quad:\quad\MM \qquadthat is: \mathcal M $\Mult$ \quad:\quad\Mult \qquadMultiplication as a Primitive Recursive Function‎ $\multiset {a, b, c}$ \quad:\quad\multiset {a, b, c} \qquadMultiset $\map \nec P$ \quad:\quad\map \nec P \qquadit is necessary that P $\NegativeBinomial {n} {p}$ \quad:\quad\NegativeBinomial {n} {p} \qquadNegative Binomial Distribution $\Nil {R}$ \quad:\quad\Nil {R} \qquadNilradical of Ring $\nint {11.98}$ \quad:\quad\nint {11.98} \qquadNearest Integer Function $\NN$ \quad:\quad\NN \qquadthat is: \mathcal N $\norm {z^2}$ \quad:\quad\norm {z^2} \qquadNorm $\O$ \quad:\quad\O \qquadEmpty Set $\OO$ \quad:\quad\OO \qquadthat is: \mathcal O $\oo$ \quad:\quad\oo \qquadthat is: \mathcal o $\oldpence$ \quad:\quad\oldpence \qquadold pence $\On$ \quad:\quad\On \qquadClass of All Ordinals $\openint {a} {b}$ \quad:\quad\openint {a} {b} \qquadOpen Interval $\Orb S$ \quad:\quad\Orb S \qquadOrbit $\Ord {S}$ \quad:\quad\Ord {S} \qquad$$S$ is an Ordinal $\order {G}$ $\quad:\quad$\order {G} $\qquad$Order of Structure, and so on $\ot$ $\quad:\quad$\ot $\qquad$Order Type $\Out {G}$ $\quad:\quad$\Out {G} $\qquad$Group of Outer Automorphisms $\paren {a + b + c}$ $\quad:\quad$\paren {a + b + c} $\qquad$Parenthesis $\ph z$ $\quad:\quad$\ph z $\qquad$Phase $\Poisson {\lambda}$ $\quad:\quad$\Poisson {\lambda} $\qquad$Poisson Distribution $\polar {r, \theta}$ $\quad:\quad$\polar {r, \theta} $\qquad$Polar Form of Complex Number $\map \pos P$ $\quad:\quad$\map \pos P $\qquad$it is possible that $P$ $\pounds$ $\quad:\quad$\pounds $\qquad$Pound Sterling $\powerset {S}$ $\quad:\quad$\powerset {S} $\qquad$Power Set $\PP$ $\quad:\quad$\PP $\qquad$that is: \mathcal P $\map {\pr_j} {F}$ $\quad:\quad$\map {\pr_j} {F} $\qquad$Projection $\Preimg {f}$ $\quad:\quad$\Preimg {f} $\qquad$Preimage of Mapping $\map {\proj_\mathbf v} {\mathbf u}$ $\quad:\quad$\map {\proj_\mathbf v} {\mathbf u} $\qquad$Vector Projection $\PV$ $\quad:\quad$\PV $\qquad$Cauchy Principal Value $\QQ$ $\quad:\quad$\QQ $\qquad$that is: \mathcal Q $\radians$ $\quad:\quad$\radians $\qquad$Radian $\Rad$ $\quad:\quad$\Rad $\qquad$Radical of Ideal of Ring $\ds \int \map f x \rd x$ $\quad:\quad$\ds \int \map f x \rd x $\qquad$Roman $\d$ for use in Integrals $\rD$ $\quad:\quad$\rD $\qquad$Differential Operator $y \rdelta x$ $\quad:\quad$y \rdelta x $\qquad$$\delta$ operator for use in sums $30 \rankine$ $\quad:\quad$30 \rankine $\qquad$Degrees Rankine $\map \Re z$ $\quad:\quad$\map \Re z $\qquad$Real Part $\relcomp {S} {A}$ $\quad:\quad$\relcomp {S} {A} $\qquad$Relative Complement $\rem$ $\quad:\quad$\rem $\qquad$Remainder $\Res {f} {z_0}$ $\quad:\quad$\Res {f} {z_0} $\qquad$Residue $\rightparen {a + b + c}$ $\quad:\quad$\rightparen {a + b + c} $\qquad$Parenthesis (right only) $\rightset {a, b, c}$ $\quad:\quad$\rightset {a, b, c} $\qquad$Conventional set notation (right only) $\Rng {f}$ $\quad:\quad$\Rng {f} $\qquad$Range of Mapping $\RR$ $\quad:\quad$\RR $\qquad$that is: \mathcal R $\sech$ $\quad:\quad$\sech $\qquad$Hyperbolic Secant $\Sech$ $\quad:\quad$\Sech $\qquad$Hyperbolic Secant $53 \seconds$ $\quad:\quad$53 \seconds $\qquad$Seconds of Angle or Seconds of Time $\sequence {a_n}$ $\quad:\quad$\sequence {a_n} $\qquad$Sequence $\set {a, b, c}$ $\quad:\quad$\set {a, b, c} $\qquad$Conventional set notation $\ShiftedGeometric {p}$ $\quad:\quad$\ShiftedGeometric {p} $\qquad$Shifted Geometric Distribution $\shillings$ $\quad:\quad$\shillings $\qquad$shillings $\Si$ $\quad:\quad$\Si $\qquad$Sine Integral Function $\Sinh$ $\quad:\quad$\Sinh $\qquad$Hyperbolic Sine $\size {x}$ $\quad:\quad$\size {x} $\qquad$Absolute Value, and so on $\SL {n, \R}$ $\quad:\quad$\SL {n, \R} $\qquad$Special Linear Group $\sn u$ $\quad:\quad$\sn u $\qquad$Elliptic Function $\span$ $\quad:\quad$\span $\qquad$Linear Span $\Spec {R}$ $\quad:\quad$\Spec {R} $\qquad$Spectrum of Ring $\sqbrk {a}$ $\quad:\quad$\sqbrk {a}  $\SS$ $\quad:\quad$\SS $\qquad$that is: \mathcal S $\Stab x$ $\quad:\quad$\Stab x $\qquad$Stabilizer $\stratgame {N} {A_i} {\succsim_i}$ $\quad:\quad$\stratgame {N} {A_i} {\succsim_i} $\qquad$Strategic Game $\struct {G, \circ}$ $\quad:\quad$\struct {G, \circ} $\qquad$Algebraic Structure $\StudentT {k}$ $\quad:\quad$\StudentT {k} $\qquad$Student's t-Distribution $\SU {n}$ $\quad:\quad$\SU {n} $\qquad$Unimodular Unitary Group $\Succ$ $\quad:\quad$\Succ $\qquad$Successor Function $\supp$ $\quad:\quad$\supp $\qquad$Support $\Syl {p} {N}$ $\quad:\quad$\Syl {p} {N} $\qquad$Sylow $p$-Subgroup $\symdif$ $\quad:\quad$\symdif $\qquad$Symmetric Difference $\T$ $\quad:\quad$\T $\qquad$True $\Tanh$ $\quad:\quad$\Tanh $\qquad$Hyperbolic Tangent $\tr$ $\quad:\quad$\tr $\qquad$Trace $\TT$ $\quad:\quad$\TT $\qquad$that is: \mathcal T $\tuple {a, b, c}$ $\quad:\quad$\tuple {a, b, c} $\qquad$Ordered Tuple $\UU$ $\quad:\quad$\UU $\qquad$that is: \mathcal U $\valueat {\dfrac {\delta y} {\delta x} } {x \mathop = \xi}$ $\quad:\quad$\valueat {\dfrac {\delta y} {\delta x} } {x \mathop = \xi}  $\var {X}$ $\quad:\quad$\var {X} $\qquad$Variance $\vers \theta$ $\quad:\quad$\vers \theta $\qquad$Versed Sine $\VV$ $\quad:\quad$\VV $\qquad$that is: \mathcal V $\weakconv$ $\quad:\quad$\weakconv $\qquad$Weak Convergence $\weakstarconv$ $\quad:\quad$\weakstarconv $\qquad$Weak-$*$ Convergence $\WW$ $\quad:\quad$\WW $\qquad$that is: \mathcal W $\XX$ $\quad:\quad$\XX $\qquad$that is: \mathcal X $\YY$ $\quad:\quad$\YY $\qquad$that is: \mathcal Y $\ZZ$ $\quad:\quad$\ZZ $\qquad$that is: \mathcal Z