由于之前写学习笔记时总是不会输入数学符号,这时候就跑到搜索引擎里面去搜索,再复制。索性自己抄写一遍,后续再需要复制可以来这里。

参考 Art of Problem Solving

Operators

Symbol Command Symbol Command Symbol Command
±\pm \pm \mp \mp ×\times \times
÷\div \div \cdot \cdot \ast \ast
\star \star \dagger \dagger \ddagger \ddagger
⨿\amalg \amalg \cap \cap \cup \cup
\uplus \uplus \sqcap \sqcap \sqcup \sqcup
\vee \vee \wedge \wedge \oplus \oplus
\ominus \ominus \otimes \otimes \circ \circ
\bullet \bullet \diamond \diamond \lhd \lhd
\rhd \rhd \unlhd \unlhd \unrhd \unrhd
\oslash \oslash \odot \odot \bigcirc \bigcirc
\triangleleft \triangleleft \Diamond \Diamond \bigtriangleup \bigtriangleup
\bigtriangledown \bigtriangledown \Box \Box \triangleright \triangleright
\setminus \setminus \wr \wr x\sqrt{x} \sqrt{x}
xx^{\circ} x^{\circ} \triangledown \triangledown xn\sqrt[n]{x} \sqrt[n]{x}
axa^x a^x axyza^{xyz} a^{xyz} axa_x a_x

Relations

Symbol Command Symbol Command Symbol Command
\le \le \ge \ge \neq \neq
\sim \sim \ll \ll \gg \gg
\doteq \doteq \simeq \simeq \subset \subset
\supset \supset \approx \approx \asymp \asymp
\subseteq \subseteq \supseteq \supseteq \cong \cong
\smile \smile \sqsubset \sqsubset \sqsupset \sqsupset
\equiv \equiv \frown \frown \sqsubseteq \sqsubseteq
\sqsupseteq \sqsupseteq \propto \propto \bowtie \bowtie
\in \in \ni \ni \prec \prec
\succ \succ \vdash \vdash \dashv \dashv
\preceq \preceq \succeq \succeq \models \models
\perp \perp \parallel \parallel
\mid \mid \bumpeq \bumpeq

Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an “n” between the \ and the word. Here are a couple examples, plus many other negations; it works for many of the many others as well.

Symbol Command Symbol Command Symbol Command
\nmid \nmid \nleq \nleq \ngeq \ngeq
\nsim \nsim \ncong \ncong \nparallel \nparallel
\not< \not< \not> \not> \not= \not= or \neq or \ne
≰\not\le \not\le ≱\not\ge \not\ge ≁\not\sim \not\sim
≉\not \approx \not\approx ≇\not\cong \not\cong ≢\not\equiv \not\equiv
∦\not\parallel \not\parallel \nless \nless \ngtr \ngtr
\lneq \lneq \gneq \gneq \lnsim \lnsim
\lneqq \lneqq \gneqq \gneqq

To use other relations not listed here, such as =, >, and <, in LaTeX, you must use the symbols on your keyboard, as they are not available in LaTeX\LaTeX.

Greek Letters

Lowercase Letters

Symbol Command Symbol Command Symbol Command Symbol Command
α\alpha \alpha β\beta \beta γ\gamma \gamma δ\delta \delta
ϵ\epsilon \epsilon ε\varepsilon \varepsilon ζ\zeta \zeta η\eta \eta
θ\theta \theta ϑ\vartheta \vartheta ι\iota \iota κ\kappa \kappa
λ\lambda \lambda μ\mu \mu ν\nu \nu ξ\xi \xi
π\pi \pi ϖ\varpi \varpi ρ\rho \rho ϱ\varrho \varrho
σ\sigma \sigma ς\varsigma \varsigma τ\tau \tau υ\upsilon \upsilon
ϕ\phi \phi φ\varphi \varphi χ\chi \chi ψ\psi \psi
ω\omega \omega

Capital Letters

Symbol Command Symbol Command Symbol Command Symbol Command
Γ\Gamma \Gamma Δ\Delta \Delta Θ\Theta \Theta Λ\Lambda \Lambda
Ξ\Xi \Xi Π\Pi \Pi Σ\Sigma \Sigma Υ\Upsilon \Upsilon
Φ\Phi \Phi Ψ\Psi \Psi Ω\Omega \Omega

Arrows

Symbol Command Symbol Command
\gets \gets \to \to
\leftarrow \leftarrow \Leftarrow \Leftarrow
\rightarrow \rightarrow \Rightarrow \Rightarrow
\leftrightarrow \leftrightarrow \Leftrightarrow \Leftrightarrow
\mapsto \mapsto \hookleftarrow \hookleftarrow
\leftharpoonup \leftharpoonup \leftharpoondown \leftharpoondown
\rightleftharpoons \rightleftharpoons \longleftarrow \longleftarrow
\Longleftarrow \Longleftarrow \longrightarrow \longrightarrow
\Longrightarrow \Longrightarrow \longleftrightarrow \longleftrightarrow
\Longleftrightarrow \Longleftrightarrow \longmapsto \longmapsto
\hookrightarrow \hookrightarrow \rightharpoonup \rightharpoonup
\rightharpoondown \rightharpoondown \leadsto \leadsto
\uparrow \uparrow \Uparrow \Uparrow
\downarrow \downarrow \Downarrow \Downarrow
\updownarrow \updownarrow \Updownarrow \Updownarrow
\nearrow \nearrow \searrow \searrow
\swarrow \swarrow \nwarrow \nwarrow
AB\overrightarrow{AB} \overrightarrow{AB} AB\overleftarrow{AB} \overleftarrow{AB}
AB\overleftrightarrow{AB} \overleftrightarrow{AB}

(For those of you who hate typing long strings of letters, \iff and \implies can be used in place of \Longleftrightarrow and \Longrightarrow respectively.)

Dots

Symbol Command Symbol Command
\cdot \cdot \vdots \vdots
\dots \dots \ddots \ddots
\cdots \cdots \iddots \iddots

Accents

Symbol Command Symbol Command Symbol Command
x^\hat{x} \hat{x} xˇ\check{x} \check{x} x˙\dot{x} \dot{x}
x˘\breve{x} \breve{x} xˊ\acute{x} \acute{x} x¨\ddot{x} \ddot{x}
xˋ\grave{x} \grave{x} x~\tilde{x} \tilde{x} x˚\mathring{x} \mathring{x}
xˉ\bar{x} \bar{x} x\vec{x} \vec{x}

When applying accents to i and j, you can use \imath and \jmath to keep the dots from interfering with the accents:

Symbol Command Symbol Command
ȷ\vec{\jmath} \vec{\jmath} ı~\tilde{\imath} \tilde{\imath}

\tilde and \hat have wide versions that allow you to accent an expression:

Symbol Command Symbol Command
7+x^\widehat{7+x} \widehat{7+x} abc~\widetilde{abc} \widetilde{abc}

Others

Symbol Command Symbol Command Symbol Command
\infty \infty \triangle \triangle \angle \angle
\aleph \aleph \hbar \hbar ı\imath \imath
ȷ\jmath \jmath \ell \ell \wp \wp
\Re \Re \Im \Im \mho \mho
\prime \prime \emptyset \emptyset \nabla \nabla
\surd \surd \partial \partial \top \top
\bot \bot \vdash \vdash \dashv \dashv
\forall \forall \exists \exists ¬\neg \neg
\flat \flat \natural \natural \sharp \sharp
\\backslash \backslash \Box \Box \Diamond \Diamond
\clubsuit \clubsuit \diamondsuit \diamondsuit \heartsuit \heartsuit
\spadesuit \spadesuit \Join \Join \blacksquare \blacksquare
\diamondsuit \diamondsuit ©\copyright \copyright \underarc{XYZ} \underarc{XYZ}
\heartsuit \heartsuit \overarc{ABC} \overarc{ABC} \cup \cup
\S \S \P \P \Vdash \Vdash
£\pounds \pounds \in \in \vDash \vDash
\bigstar \bigstar     \implies \implies
\square \square
\smiley \smiley
R\mathbb{R} \mathbb{R} (represents all real numbers)
\checkmark \checkmark
\cancer \cancer

Note: \cancer and \overarc{ABC} do not work in the classroom.

Command Symbols

Some symbols are used in commands, so they need to be treated in a special way.

Symbol Command Symbol Command Symbol Command Symbol Command
\textdollar \textdollar or \$ &\& \& %\% \% #\# \#
_\_ \_ {\{ \{ }\} \} \\backslash \backslash

(Warning: Using $ for \textdollar will result in $$. This is a bug as far as we know. Depending on the version of LaTeX\LaTeX this is not always a problem.)

European Language Symbols

Symbol Command Symbol Command Symbol Command Symbol Command
{\oe} {\oe} {\ae} {\ae} {\o} {\o}
{\OE} {\OE} {\AE} {\AE} {\AA} {\AA} {\O} {\O}
{\l} {\l} {\ss} {\ss} !‘\text{!`} | !`
{\L} {\L} {\SS} {\SS}

Bracketing Symbols

In mathematics, sometimes we need to enclose expressions in brackets, braces or parentheses. Some of these work just as you’d imagine in LaTeX; type ( and ) for parentheses, [ and ] for brackets, and | and | for absolute value. However, other symbols have special commands:

Symbol Command Symbol Command Symbol Command
{\{ \{ }\} \} \| \\
\\backslash \backslash \lfloor \lfloor \rfloor \rfloor
\lceil \lceil \rceil \rceil \langle \langle
\rangle \rangle

You might notice that if you use any of these to typeset an expression that is vertically large, like

(\frac{a}{x} )^2
the parentheses don’t come out the right size:

(ax)2(\frac{a}{x})^2

If we put \left and \right before the relevant parentheses, we get a prettier expression:

\left(\frac{a}{x} \right)^2
gives

(ax)2\left(\frac{a}{x} \right)^2

For systems of equations or piecewise functions, use the cases environment:

f(x) = \begin{cases} x^2 & x \ge 0 \\ x & x < 0 \end{cases}

which gives

f(x)={x2x0xx<0f(x) = \begin{cases} x^2 & x \ge 0 \\ x & x < 0 \end{cases}

In addition to the \left and \right commands, when doing floor or ceiling functions with fractions, using

\left\lceil\frac{x}{y}\right\rceil

and \left\lfloor\frac{x}{y}\right\rfloor

gives both xy\left\lceil\frac{x}{y}\right\rceil and xy\left\lfloor\frac{x}{y}\right\rfloor, respectively.

And, if you type this

\underbrace{a_0+a_1+a_2+\cdots+a_n}_{x}

Gives

a0+a1+a2++anx\underbrace{a_0+a_1+a_2+\cdots+a_n}_{x}

Or

\overbrace{a_0+a_1+a_2+\cdots+a_n}^{x}

Gives

a0+a1+a2++anx\overbrace{a_0+a_1+a_2+\cdots+a_n}^{x}

\left and \right can also be used to resize the following symbols:

Symbol Command Symbol Command Symbol Command
\uparrow \uparrow \downarrow \downarrow \updownarrow \updownarrow
\Uparrow \Uparrow \Downarrow \Downarrow \Updownarrow \Updownarrow

Multi-Size Symbols

Some symbols render differently in inline math mode and in display mode. Display mode occurs when you use […] or $$…$$, or environments like \begin{equation}…\end{equation}, \begin{align}…\end{align}. Read more in the commands section of the guide about how symbols which take arguments above and below the symbols, such as a summation symbol, behave in the two modes.

In each of the following, the two images show the symbol in display mode, then in inline mode.

Symbol Command Symbol Command Symbol Command
\sum \textstyle\sum \sum \int \textstyle\int \int \oint \textstyle\oint \oint
\prod \textstyle\prod \prod \coprod \textstyle\coprod \coprod \bigcap \textstyle\bigcap \bigcap
\bigcup \textstyle\bigcup \bigcup \bigsqcup \textstyle\bigsqcup \bigsqcup \bigvee \textstyle\bigvee \bigvee
\bigwedge \textstyle\bigwedge \bigwedge \bigodot \textstyle\bigodot \bigodot \bigotimes \textstyle\bigotimes \bigotimes
\bigoplus \textstyle\bigoplus \bigoplus \biguplus \textstyle\biguplus \biguplus