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[LaTeX] Math Symbols

category: Writing | course: LaTeX Math | difficulty:

I’ve already subtly mentioned that LaTeX uses a set of rules to determine the amount of spacing around symbols. It supports a humongous amount of symbols, which means I’m going to use those rules as a way to group them and keep this page clean.

Basically, LaTeX has placed symbols in 7 different groups or levels, which each have their own fixed spacing rules. The Greek symbols from last chapter, for example, are from the first level, and always have the default amount of spacing on both left and right side. All default letters and numbers, spacing commands, and the math accents we’ve discussed, are also in level 1.

Most of these symbols need the amssymb package. I, personally, always include it just to be sure.

Level 1 – Simple Symbols

Simple symbols don’t have any advanced functionality – just type the command and the symbol is displayed. Some of them also have no predefined function in mathematics.

VisualCommandVisualCommand
\( \aleph \)\aleph \( \mho \)\mho
\( \beth \)\beth \( \partial \)\partial
\( \daleth \)\daleth \( \wp \)\wp
\( \gimel \)\gimel \( \circledS \)\circledS
\( \complement \)\complement \( \Bbbk \)\Bbbk
\( \ell \)\ell \( \Finv \)\Finv
\( \eth \)\eth \( \Game \)\Game
\( \hbar \)\hbar \( \Im \)\Im
\( \hslash \)\hslash \( \Re \)\Re
VisualCommandVisualCommand
\( \# \)\# \( \infty \)\infty
\( \angle \)\angle \( \lozenge \)\lozenge
\( \backprime \)\backprime \( \measuredangle \)\measuredangle
\( \bigstar \)\bigstar \( \nabla \)\nabla
\( \blacklozenge \)\blacklozenge \( \natural \)\natural
\( \blacksquare \)\blacksquare \( \neg \)\neg
\( \blacktriangle \)\blacktriangle \( \nexists \)\nexists
\( \blacktriangledown \)\blacktriangledown \( \prime \)\prime
\( \bot \)\bot \( \S \)\S
\( \clubsuit \)\clubsuit \( \sharp \)\sharp
\( \diagdown \)\diagdown \( \spadesuit \)\spadesuit
\( \diagup \)\diagup \( \sphericalangle \)\sphericalangle
\( \diamondsuit \)\diamondsuit \( \square p \)\square p
\( \emptyset \)\emptyset \( \surd \)\surd
\( \exists \)\exists \( \top \)\top
\( \flat \)\flat \( \triangle \)\triangle
\( \forall \)\forall \( \triangledown \)\triangledown
\( \heartsuit \)\heartsuit \( \varnothing \)\varnothing

Level 2 – Functions

Contains the big symbols and functions we’ve discussed, with those fancy subscripts and superscripts. Nothing new here, let’s continue!

Level 3 – Binary Operators

Binary operators perform an operation using the two letters/symbols around it, which means there’s not much space around them.

VisualCommandVisualCommand
\( * \)* \( \divideontimes \)\divideontimes
\( + \)+ \( \dotplus \)\dotplus
\( - \)- \( \doublebarwedge \)\doublebarwedge
\( \amalg \)\amalg \( \gtrdot \)\gtrdot
\( \ast \)\ast \( \intercal \)\intercal
\( \barwedge \)\barwedge \( \leftthreetimes \)\leftthreetimes
\( \bigcirc \)\bigcirc \( \lessdot \)\lessdot
\( \bigtriangledown \)\bigtriangledown \( \ltimes \)\ltimes
\( \bigtriangleup \)\bigtriangleup \( \mp \)\mp
\( \boxdot \)\boxdot \( \odot \)\odot
\( \boxminus \)\boxminus \( \ominus \)\ominus
\( \boxplus \)\boxplus \( \oplus \)\oplus
\( \boxtimes \)\boxtimes \( \oslash \)\oslash
\( \bullet \)\bullet \( \otimes \)\otimes
\( \cap \)\cap \( \pm \)\pm
\( \Cap \)\Cap \( \rightthreetimes \)\rightthreetimes
\( \cdot \)\cdot \( \rtimes \)\rtimes
\( \centerdot \)\centerdot \( \setminus \)\setminus
\( \circ \)\circ \( \smallsetminus \)\smallsetminus
\( \circledast \)\circledast \( \sqcap \)\sqcap
\( \circledcirc \)\circledcirc \( \sqcup \)\sqcup
\( \circleddash \)\circleddash \( \star \)\star
\( \cup \)\cup \( \times \)\times
\( \Cup \)\Cup \( \triangleleft \)\triangleleft
\( \curlyvee \)\curlyvee \( \triangleright \)\triangleright
\( \curlywedge \)\curlywedge \( \uplus \)\uplus
\( \dagger \)\dagger \( \vee \)\vee
\( \ddagger \)\ddagger \( \veebar \)\veebar
\( \diamond \)\diamond \( \wedge \)\wedge
\( \div \)\div \( \wr \)\wr

Level 4 – Relations

Relational operators define a relationship between what’s around it, such as equality or a specific inequality. They also contain the symbols often used for displaying relationships – arrows.

Relational/Comparison Operators
VisualCommandVisualCommand
\( < \)<\( \lll \)\lll
\( = \)=\( \lnapprox \)\lnapprox
\( > \)>\( \lneq \)\lneq
\( \approx \)\approx\( \lneqq \)\lneqq
\( \approxeq \)\approxeq\( \lnsim \)\lnsim
\( \asymp \)\asymp\( \lvertneqq \)\lvertneqq
\( \backsim \)\backsim\( \ncong \)\ncong
\( \backsimeq \)\backsimeq\( \neq \)\neq
\( \bumpeq \)\bumpeq\( \ngeq \)\ngeq
\( \Bumpeq \)\Bumpeq\( \ngeqq \)\ngeqq
\( \circeq \)\circeq\( \ngeqslant \)\ngeqslant
\( \cong \)\cong\( \ngtr \)\ngtr
\( \curlyeqprec \)\curlyeqprec\( \nleq \)\nleq
\( \curlyeqsucc \)\curlyeqsucc\( \nleqq \)\nleqq
\( \doteq \)\doteq\( \nleqslant \)\nleqslant
\( \doteqdot \)\doteqdot\( \nless \)\nless
\( \eqcirc \)\eqcirc\( \nprec \)\nprec
\( \eqsim \)\eqsim\( \npreceq \)\npreceq
\( \eqslantgtr \)\eqslantgtr\( \nsim \)\nsim
\( \eqslantless \)\eqslantless\( \nsucc \)\nsucc
\( \equiv \)\equiv\( \nsucceq \)\nsucceq
\( \fallingdotseq \)\fallingdotseq\( \prec \)\prec
\( \geq \)\geq\( \precapprox \)\precapprox
\( \geqq \)\geqq\( \preccurlyeq \)\preccurlyeq
\( \geqslant \)\geqslant\( \preceq \)\preceq
\( \gg \)\gg\( \precnapprox \)\precnapprox
\( \ggg \)\ggg\( \precneqq \)\precneqq
\( \gnapprox \)\gnapprox\( \precnsim \)\precnsim
\( \gneq \)\gneq\( \precsim \)\precsim
\( \gneqq \)\gneqq\( \risingdotseq \)\risingdotseq
\( \gnsim \)\gnsim\( \sim \)\sim
\( \gtrapprox \)\gtrapprox\( \simeq \)\simeq
\( \gtreqless \)\gtreqless\( \succ \)\succ
\( \gtreqqless \)\gtreqqless\( \succapprox \)\succapprox
\( \gtrless \)\gtrless\( \succcurlyeq \)\succcurlyeq
\( \gtrsim \)\gtrsim\( \succeq \)\succeq
\( \gvertneqq \)\gvertneqq\( \succnapprox \)\succnapprox
\( \leq \)\leq\( \succneqq \)\succneqq
\( \leqq \)\leqq\( \succnsim \)\succnsim
\( \leqslant \)\leqslant\( \succsim \)\succsim
\( \lessapprox \)\lessapprox\( \thickapprox \)\thickapprox
\( \lesseqgtr \)\lesseqgtr\( \thicksim \)\thicksim
\( \lesseqqgtr \)\lesseqqgtr\( \triangleq \)\triangleeq
\( \lessgtr \)\lessgtr
\( \lesssim \)\lesssim
\( \ll \)\ll
Arrows
VisualCommandVisualCommand
\( \circlearrowleft \)\circlearrowleft\( \Lsh \)\Lsh
\( \circlearrowright \)\circlearrowright\( \mapsto \)\mapsto
\( \curvearrowleft \)\curvearrowleft\( \multimap \)\multimap
\( \curvearrowright \)\curvearrowright\( \nLeftarrow \)\nLeftarrow
\( \downdownarrows \)\downdownarrows\( \nLeftrightarrow \)nLeftrightarrow
\( \downharpoonleft \)\downharpoonleft\( \nRightarrow \)\nRightarrow
\( \downharpoonright \)\downharpoonright\( \nearrow \)\nearrow
\( \hookleftarrow \)\hookleftarrow\( \nleftarrow \)\nleftarrow
\( \hookrightarrow \)\hookrightarrow\( \nleftrightarrow \)\nleftrightarrow
\( \leftarrow \)\leftarrow\( \nrightarrow \)\nrightarrow
\( \Leftarrow \)\Leftarrow\( \nwarrow \)\nwarrow
\( \leftarrowtail \)\leftarrowtail\( \rightarrow \)\rightarrow
\( \leftharpoondown \)\leftharpoondown\( \Rightarrow \)\Rightarrow
\( \leftharpoonup \)\leftharpoonup\( \rightarrowtail \)\rightarrowtail
\( \leftleftarrows \)\leftleftarrows\( \rightharpoondown \)\rightharpoondown
\( \leftrightarrow \)\leftrightarrow\( \rightharpoonup \)\rightharpoonup
\( \Leftrightarrow \)\Leftrightarrow\( \rightleftarrows \)\rightleftarrows
\( \leftrightarrows \)\leftrightarrows\( \rightleftharpoons \)\rightleftharpoons
\( \leftrightharpoons \)\leftrightharpoons\( \rightrightarrows \)\rightrightarrows
\( \leftrightsquigarrow \)\leftrightsquigarrow\( \rightsquigarrow \)\rightsquigarrow
\( \Lleftarrow \)\Lleftarrow\( \Rrightarrow \)\Rrightarrow
\( \longleftarrow \)\longleftarrow\( \Rsh \)\Rsh
\( \Longleftarrow \)\Longleftarrow\( \searrow \)\searrow
\( \longleftrightarrow \)\longleftrightarrow \( \swarrow \)\swarrow
\( \Longleftrightarrow \)\Longleftrightarrow\( \twoheadleftarrow \)\twoheadleftarrow
\( \longmapsto \)\longmapsto\( \twoheadrightarrow \)\twoheadrightarrow
\( \longrightarrow \)\longrightarrow\( \upharpoonleft \)\upharpoonleft
\( \Longrightarrow \)\Longrightarrow\( \upharpoonright \)\upharpoonright
\( \looparrowleft \)\looparrowleft\( \upuparrows \)\upuparrows
\( \looparrowright \)\looparrowright
Others
VisualCommandVisualCommand
\( \backepsilon \)\backepsilon\( \smallfrown \)\smallfrown
\( \because \)\because\( \smallsmile \)\smallsmile
\( \between \)\between\( \smile \)\smile
\( \blacktriangleleft \)\blacktriangleleft\( \sqsubset \)\sqsubset
\( \blacktriangleright \)\blacktriangleright\( \sqsubseteq \)\sqsubseteq
\( \bowtie \)\bowtie\( \sqsupset \)\sqsupset
\( \dashv \)\dashv\( \sqsupseteq \)\sqsupseteq
\( \frown \)\frown\( \subset \)\subset
\( \in \)\in\( \Subset \)\Subset
\( \mid \)\mid\( \subseteq \)\subseteq
\( \models \)\models\( \subseteqq \)\subseteqq
\( \ni \)\ni\( \subsetneq \)\subsetneq
\( \nmid \)\nmid\( \subsetneqq \)\subsetneqq
\( \notin \)\notin\( \supset \)\supset
\( \nparallel \)\nparallel\( \Supset \)\Supset
\( \nshortmid \)\nshortmid\( \supseteq \)\supseteq
\( \nshortparallel \)\nshortparallel\( \supseteqq \)\supseteqq
\( \nsubseteq \)\nsubseteq\( \supsetneq \)\supsetneq
\( \nsubseteqq \)\nsubseteqq\( \supsetneqq \)\supsetneqq
\( \nsupseteq \)\nsupseteq\( \therefore \)\therefore
\( \nsupseteqq \)\nsupseteqq\( \trianglelefteq \)\trianglelefteq
\( \ntriangleleft \)\ntriangleleft\( \trianglerighteq \)\trianglerighteq
\( \ntrianglelefteq \)\ntrianglelefteq\( \varpropto \)\varpropto
\( \ntriangleright \)\ntriangleright\( \varsubsetneq \)\varsubsetneq
\( \ntrianglerighteq \)\ntrianglerighteq\( \varsubsetneqq \)\varsubsetneqq
\( \nvdash \)\nvdash\( \varsupsetneq \)\varsupsetneq
\( \nVdash \)\nVdash\( \varsupsetneqq \)\varsupsetneqq
\( \nvDash \)\nvDash\( \vartriangle \)\vartriangle
\( \nVDash \)\nVDash\( \vartriangleleft \)\vartriangleleft
\( \parallel \)\parallel\( \vartriangleright \)\vartriangleright
\( \perp \)\perp\( \vdash \)\vdash
\( \pitchfork \)\pitchfork\( \Vdash \)\Vdash
\( \propto \)\propto\( \vDash \)\vDash
\( \shortmid \)\shortmid\( \Vvdash \)\Vvdash
\( \shortparallel \)\shortparallel

Level 5 & 6 – Left/Open and Right/Close Operators

We’ve already discussed these in depth in the Delimiters chapter. The only thing new here is vertical arrows that have the ability to scale with whatever they are around.

VisualCommandVisualCommand
\( \uparrow \)\uparrow \( \Downarrow \)\Downarrow
\( \Uparrow \)\uparrow \( \updownarrow \)\updownarrow
\( \downarrow \)\downarrow \( \Updownarrow \)\Updownarrow

Level 7 – Punctuation Symbols

This level, not surprisingly, contains all regular symbols used for punctuation. On top of that, there are some commands that generate dots, which are more useful than you think.

VisualCommandVisualCommand
\( \dotsb \)\dotsb \( \ddots \)\ddots
\( \vdots \)\vdots \( \dotsc \)\dotsc
\( \dotsi \)\dotsi \( \dotsm \)\dotsm
\( \dotso \)\dotso
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