I’ve already subtly mentioned that LaTeX uses a very complex set of rules to determine the amount of spacing around symbols.It also supports a humongous number of symbols.

This means I will give an incomplete summary of those spacing rules, so I can use them to group all symbols cleanly.

Basically, LaTeX has placed symbols in 7 different levels. Each level has its own fixed spacing rules.

The Greek symbols from last chapter, for example, are from the first level. They always have the default amount of spacing on both left and right side. All letters and numbers, spacing commands, and math accents 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.

Basic

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

Specialized

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. See: Sums, Integrals and More

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/Right and Open/Close

We’ve already discussed these in-depth in the Delimiters chapter. The only thing new here are 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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