Notation Reference

This chapter is a reference. Skim it now, bookmark it, and come back when you need a specific symbol. Every symbol shown here works with amsmath and amssymb loaded.

This LaTeX math symbols reference is the chapter you bookmark rather than read: sets, logic, calculus, algebra, and analysis notation, every symbol shown with its command and rendered output. Skim once now so you know what lives here, then return when you need that one arrow.

Greek Alphabet

• Name: Alpha | Lower: \alpha | Output: \( \alpha \) | Upper: — | Output: \( A \) | Variant: —

• Name: Beta | Lower: \beta | Output: \( \beta \) | Upper: — | Output: \( B \) | Variant: —

• Name: Gamma | Lower: \gamma | Output: \( \gamma \) | Upper: \Gamma | Output: \( \Gamma \) | Variant: —

• Name: Delta | Lower: \delta | Output: \( \delta \) | Upper: \Delta | Output: \( \Delta \) | Variant: —

• Name: Epsilon | Lower: \epsilon | Output: \( \epsilon \) | Upper: — | Output: \( E \) | Variant: \( \varepsilon \)

• Name: Zeta | Lower: \zeta | Output: \( \zeta \) | Upper: — | Output: \( Z \) | Variant: —

• Name: Eta | Lower: \eta | Output: \( \eta \) | Upper: — | Output: \( H \) | Variant: —

• Name: Theta | Lower: \theta | Output: \( \theta \) | Upper: \Theta | Output: \( \Theta \) | Variant: \( \vartheta \)

• Name: Iota | Lower: \iota | Output: \( \iota \) | Upper: — | Output: \( I \) | Variant: —

• Name: Kappa | Lower: \kappa | Output: \( \kappa \) | Upper: — | Output: \( K \) | Variant: \( \varkappa \)

• Name: Lambda | Lower: \lambda | Output: \( \lambda \) | Upper: \Lambda | Output: \( \Lambda \) | Variant: —

• Name: Mu | Lower: \mu | Output: \( \mu \) | Upper: — | Output: \( M \) | Variant: —

• Name: Nu | Lower: \nu | Output: \( \nu \) | Upper: — | Output: \( N \) | Variant: —

• Name: Xi | Lower: \xi | Output: \( \xi \) | Upper: \Xi | Output: \( \Xi \) | Variant: —

• Name: Omicron | Lower: \( o \) | Output: \( o \) | Upper: — | Output: \( O \) | Variant: —

• Name: Pi | Lower: \pi | Output: \( \pi \) | Upper: \Pi | Output: \( \Pi \) | Variant: \( \varpi \)

• Name: Rho | Lower: \rho | Output: \( \rho \) | Upper: — | Output: \( P \) | Variant: \( \varrho \)

• Name: Sigma | Lower: \sigma | Output: \( \sigma \) | Upper: \Sigma | Output: \( \Sigma \) | Variant: \( \varsigma \)

• Name: Tau | Lower: \tau | Output: \( \tau \) | Upper: — | Output: \( T \) | Variant: —

• Name: Upsilon | Lower: \upsilon | Output: \( \upsilon \) | Upper: \Upsilon | Output: \( \Upsilon \) | Variant: —

• Name: Phi | Lower: \phi | Output: \( \phi \) | Upper: \Phi | Output: \( \Phi \) | Variant: \( \varphi \)

• Name: Chi | Lower: \chi | Output: \( \chi \) | Upper: — | Output: \( X \) | Variant: —

• Name: Psi | Lower: \psi | Output: \( \psi \) | Upper: \Psi | Output: \( \Psi \) | Variant: —

• Name: Omega | Lower: \omega | Output: \( \omega \) | Upper: \Omega | Output: \( \Omega \) | Variant: —

  Binary Operators

• Command: + | Symbol: \( + \)

• Command: - | Symbol: \( – \)

• Command: \pm | Symbol: \( \pm \)

• Command: \mp | Symbol: \( \mp \)

• Command: \times | Symbol: \( \times \)

• Command: \div | Symbol: \( \div \)

• Command: \ast | Symbol: \( \ast \)

• Command: \star | Symbol: \( \star \)

• Command: \circ | Symbol: \( \circ \)

• Command: \bullet | Symbol: \( \bullet \)

• Command: \cap | Symbol: \( \cap \)

• Command: \cup | Symbol: \( \cup \)

• Command: \sqcap | Symbol: \( \sqcap \)

• Command: \sqcup | Symbol: \( \sqcup \)

• Command: \wedge | Symbol: \( \wedge \)

• Command: \vee | Symbol: \( \vee \)

• Command: \oplus | Symbol: \( \oplus \)

• Command: \ominus | Symbol: \( \ominus \)

• Command: \otimes | Symbol: \( \otimes \)

• Command: \oslash | Symbol: \( \oslash \)

• Command: \odot | Symbol: \( \odot \)

• Command: \dagger | Symbol: \( \dagger \)

• Command: \ddagger | Symbol: \( \ddagger \)

• Command: \amalg | Symbol: \( \amalg \)

• Command: \setminus | Symbol: \( \setminus \)

• Command: \wr | Symbol: \( \wr \)

• Command: \diamond | Symbol: \( \diamond \)

• Command: \bigcirc | Symbol: \( \bigcirc \)

• Command: \triangle | Symbol: \( \triangle \)

  Relations

• Command: = | Symbol: \( = \)

• Command: \neq | Symbol: \( \neq \)

• Command: < | Symbol: \( < \)

• Command: > | Symbol: \( > \)

• Command: \leq | Symbol: \( \leq \)

• Command: \geq | Symbol: \( \geq \)

• Command: \ll | Symbol: \( \ll \)

• Command: \gg | Symbol: \( \gg \)

• Command: \equiv | Symbol: \( \equiv \)

• Command: \sim | Symbol: \( \sim \)

• Command: \simeq | Symbol: \( \simeq \)

• Command: \approx | Symbol: \( \approx \)

• Command: \cong | Symbol: \( \cong \)

• Command: \doteq | Symbol: \( \doteq \)

• Command: \propto | Symbol: \( \propto \)

• Command: \models | Symbol: \( \models \)

• Command: \vdash | Symbol: \( \vdash \)

• Command: \dashv | Symbol: \( \dashv \)

• Command: \perp | Symbol: \( \perp \)

• Command: \parallel | Symbol: \( \parallel \)

• Command: \in | Symbol: \( \in \)

• Command: \notin | Symbol: \( \notin \)

• Command: \ni | Symbol: \( \ni \)

• Command: \subset | Symbol: \( \subset \)

• Command: \supset | Symbol: \( \supset \)

• Command: \subseteq | Symbol: \( \subseteq \)

• Command: \supseteq | Symbol: \( \supseteq \)

• Command: \nsubseteq | Symbol: \( \nsubseteq \)

• Command: \nsupseteq | Symbol: \( \nsupseteq \)

• Command: \sqsubset | Symbol: \( \sqsubset \)

• Command: \sqsupset | Symbol: \( \sqsupset \)

• Command: \sqsubseteq | Symbol: \( \sqsubseteq \)

• Command: \sqsupseteq | Symbol: \( \sqsupseteq \)

• Command: \prec | Symbol: \( \prec \)

• Command: \succ | Symbol: \( \succ \)

• Command: \preceq | Symbol: \( \preceq \)

• Command: \succeq | Symbol: \( \succeq \)

• Command: \mid | Symbol: \( \mid \)

• Command: \nmid | Symbol: \( \nmid \)

  Arrows

• Command: \leftarrow | Symbol: \( \leftarrow \)

• Command: \rightarrow | Symbol: \( \rightarrow \)

• Command: \leftrightarrow | Symbol: \( \leftrightarrow \)

• Command: \Leftarrow | Symbol: \( \Leftarrow \)

• Command: \Rightarrow | Symbol: \( \Rightarrow \)

• Command: \Leftrightarrow | Symbol: \( \Leftrightarrow \)

• Command: \longleftarrow | Symbol: \( \longleftarrow \)

• Command: \longrightarrow | Symbol: \( \longrightarrow \)

• Command: \Longleftarrow | Symbol: \( \Longleftarrow \)

• Command: \Longrightarrow | Symbol: \( \Longrightarrow \)

• Command: \iff | Symbol: \( \iff \)

• Command: \uparrow | Symbol: \( \uparrow \)

• Command: \downarrow | Symbol: \( \downarrow \)

• Command: \updownarrow | Symbol: \( \updownarrow \)

• Command: \Uparrow | Symbol: \( \Uparrow \)

• Command: \Downarrow | Symbol: \( \Downarrow \)

• Command: \Updownarrow | Symbol: \( \Updownarrow \)

• Command: \mapsto | Symbol: \( \mapsto \)

• Command: \longmapsto | Symbol: \( \longmapsto \)

• Command: \hookrightarrow | Symbol: \( \hookrightarrow \)

• Command: \hookleftarrow | Symbol: \( \hookleftarrow \)

• Command: \nearrow | Symbol: \( \nearrow \)

  Set Notation and Logic

• Command: \mathbb{N} | Symbol: \( \mathbb{N} \) | Meaning: Natural numbers

• Command: \mathbb{Z} | Symbol: \( \mathbb{Z} \) | Meaning: Integers

• Command: \mathbb{Q} | Symbol: \( \mathbb{Q} \) | Meaning: Rational numbers

• Command: \mathbb{R} | Symbol: \( \mathbb{R} \) | Meaning: Real numbers

• Command: \mathbb{C} | Symbol: \( \mathbb{C} \) | Meaning: Complex numbers

• Command: \emptyset | Symbol: \( \emptyset \) | Meaning: Empty set

• Command: \varnothing | Symbol: \( \varnothing \) | Meaning: Empty set (preferred)

• Command: \forall | Symbol: \( \forall \) | Meaning: For all

• Command: \exists | Symbol: \( \exists \) | Meaning: There exists

• Command: \nexists | Symbol: \( \nexists \) | Meaning: There does not exist

• Command: \neg | Symbol: \( \neg \) | Meaning: Negation

• Command: \land | Symbol: \( \land \) | Meaning: Logical and

• Command: \lor | Symbol: \( \lor \) | Meaning: Logical or

• Command: \implies | Symbol: \( \implies \) | Meaning: Implies

• Command: \impliedby | Symbol: \( \impliedby \) | Meaning: Implied by

• Command: \iff | Symbol: \( \iff \) | Meaning: If and only if

• Command: \therefore | Symbol: \( \therefore \) | Meaning: Therefore

• Command: \because | Symbol: \( \because \) | Meaning: Because

  Calculus and Analysis

• Expression: Derivative | Output: \( \frac{df}{dx} \) | Code: \frac{df}{dx}

• Expression: Partial derivative | Output: \( \frac{\partial f}{\partial x} \) | Code: \frac{\partial f}{\partial x}

• Expression: Integral | Output: \( \int_a^b f\,dx \) | Code: \int_a^b f\,dx

• Expression: Double integral | Output: \( \iint_D f\,dA \) | Code: \iint_D f\,dA

• Expression: Triple integral | Output: \( \iiint_V f\,dV \) | Code: \iiint_V f\,dV

• Expression: Contour integral | Output: \( \oint_C f\,dz \) | Code: \oint_C f\,dz

• Expression: Nabla/gradient | Output: \( \nabla f \) | Code: \nabla f

• Expression: Laplacian | Output: \( \nabla^2 f \) | Code: \nabla^2 f

• Expression: Limit | Output: \( \lim_{x\to a} \) | Code: \lim_{x\to a}

• Expression: Infinity | Output: \( \infty \) | Code: \infty

• Expression: Sum | Output: \( \sum_{n=0}^{\infty} \) | Code: \sum_{n=0}^{\infty}

• Expression: Product | Output: \( \prod_{k=1}^{n} \) | Code: \prod_{k=1}^{n}

  Accents and Decorations

• Command: \hat{a} | Output: \( \hat{a} \)

• Command: \widehat{abc} | Output: \( \widehat{abc} \)

• Command: \check{a} | Output: \( \check{a} \)

• Command: \tilde{a} | Output: \( \tilde{a} \)

• Command: \widetilde{abc} | Output: \( \widetilde{abc} \)

• Command: \acute{a} | Output: \( \acute{a} \)

• Command: \grave{a} | Output: \( \grave{a} \)

• Command: \breve{a} | Output: \( \breve{a} \)

• Command: \bar{a} | Output: \( \bar{a} \)

• Command: \overline{abc} | Output: \( \overline{abc} \)

• Command: \vec{a} | Output: \( \vec{a} \)

• Command: \dot{a} | Output: \( \dot{a} \)

• Command: \ddot{a} | Output: \( \ddot{a} \)

• Command: \dddot{a} | Output: \( \dddot{a} \)

• Command: \mathring{a} | Output: \( \mathring{a} \)

  Delimiters

• Left: ( | Symbol: \( ( \) | | Right: ) | Symbol: \( ) \)

• Left: [ | Symbol: \( [ \) | | Right: ] | Symbol: \( ] \)

• Left: \{ | Symbol: \( \{ \) | | Right: \} | Symbol: \( \} \)

• Left: \langle | Symbol: \( \langle \) | | Right: \rangle | Symbol: \( \rangle \)

• Left: \ | **Symbol:** | \( \ | **Right:** \) | Symbol: | \ | | \( \ | \)

• Left: \Vert | Symbol: \( \Vert \) | | Right: \Vert | Symbol: \( \Vert \)

• Left: \lfloor | Symbol: \( \lfloor \) | | Right: \rfloor | Symbol: \( \rfloor \)

• Left: \lceil | Symbol: \( \lceil \) | | Right: \rceil | Symbol: \( \rceil \)

  Big Operators

• Command: \sum | Symbol: \( \sum \) | | Command: \prod | Symbol: \( \prod \)

• Command: \coprod | Symbol: \( \coprod \) | | Command: \int | Symbol: \( \int \)

• Command: \iint | Symbol: \( \iint \) | | Command: \iiint | Symbol: \( \iiint \)

• Command: \oint | Symbol: \( \oint \) | | Command: \bigcup | Symbol: \( \bigcup \)

• Command: \bigcap | Symbol: \( \bigcap \) | | Command: \bigsqcup | Symbol: \( \bigsqcup \)

• Command: \bigvee | Symbol: \( \bigvee \) | | Command: \bigwedge | Symbol: \( \bigwedge \)

• Command: \bigoplus | Symbol: \( \bigoplus \) | | Command: \bigotimes | Symbol: \( \bigotimes \)

• Command: \bigodot | Symbol: \( \bigodot \) | | Command: \biguplus | Symbol: \( \biguplus \)

  Math Fonts

• Command: \mathrm{ABC} | Example: \( \mathrm{ABC} \) | Use: Upright Roman

• Command: \mathbf{ABC} | Example: \( \mathbf{ABC} \) | Use: Bold (vectors in some fields)

• Command: \mathit{ABC} | Example: \( \mathit{ABC} \) | Use: Italic (default for variables)

• Command: \mathsf{ABC} | Example: \( \mathsf{ABC} \) | Use: Sans-serif

• Command: \mathtt{ABC} | Example: \( \mathtt{ABC} \) | Use: Monospace/typewriter

• Command: \mathbb{ABC} | Example: \( \mathbb{ABC} \) | Use: Blackboard bold (number sets)

• Command: \mathcal{ABC} | Example: \( \mathcal{ABC} \) | Use: Calligraphic (operators, sheaves)

• Command: \mathfrak{ABC} | Example: \( \mathfrak{ABC} \) | Use: Fraktur (Lie algebras)

• Command: \mathscr{ABC} | Example: \( \mathscr{ABC} \) | Use: Script (requires mathrsfs)

• Command: \boldsymbol{\alpha} | Example: \( \boldsymbol{\alpha} \) | Use: Bold Greek

  Miscellaneous Symbols

• Command: \aleph | Symbol: \( \aleph \)

• Command: \beth | Symbol: \( \beth \)

• Command: \hbar | Symbol: \( \hbar \)

• Command: \ell | Symbol: \( \ell \)

• Command: \wp | Symbol: \( \wp \)

• Command: \Re | Symbol: \( \Re \)

• Command: \Im | Symbol: \( \Im \)

• Command: \partial | Symbol: \( \partial \)

• Command: \infty | Symbol: \( \infty \)

• Command: \angle | Symbol: \( \angle \)

• Command: \triangle | Symbol: \( \triangle \)

• Command: \square | Symbol: \( \square \)

• Command: \surd | Symbol: \( \surd \)

• Command: \nabla | Symbol: \( \nabla \)

• Command: \flat | Symbol: \( \flat \)

• Command: \sharp | Symbol: \( \sharp \)

  Tip: If you can’t find a symbol in these tables, try the Detexify tool (https://detexify.kirelabs.org): draw the symbol with your mouse, and it tells you the LaTeX command. It’s the fastest way to find obscure symbols.

For an even denser exam-time version, the symbol quick reference condenses this chapter to one screen. Symbols misbehaving? Check the top 20 errors first.

Quick answers to common questions: