Latex Cheatsheet (mediawiki math)

Algebraic manipulations (thanks )

3rd order logic??? @todo

= wikibooks =

arrows, dots and accents
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 Dots Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command \ldots2	\ldots 2	\vdots	\vdots	\cdots 2	\cdots 2	\ddots	\ddots

(The '2's after \ldots and \cdots are only present to make the distinction between the two clear.) Accents Symbol	Command	Symbol	Command	Symbol	Command \hat{x}	\hat{x}	\check{x}	\check{x}	\dot{x}	\dot{x} \breve{x}	\breve{x}	\acute{x}	\acute{x}	\ddot{x}	\ddot{x} \grave{x}	\grave{x}	\tilde{x}	\tilde{x}	\mathring{x}	\mathring{x} \bar{x}	\bar{x}	\vec{x}	\vec{x}

other
Dots Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command \ldots2	\ldots 2	\vdots	\vdots	\cdots 2	\cdots 2	\ddots	\ddots

(The '2's after \ldots and \cdots are only present to make the distinction between the two clear.) Accents Symbol	Command	Symbol	Command	Symbol	Command \hat{x}	\hat{x}	\check{x}	\check{x}	\dot{x}	\dot{x} \breve{x}	\breve{x}	\acute{x}	\acute{x}	\ddot{x}	\ddot{x} \grave{x}	\grave{x}	\tilde{x}	\tilde{x}	\mathring{x}	\mathring{x} \bar{x}	\bar{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 \vec{\jmath}	\vec{\jmath}	\tilde{\imath}	\tilde{\imath}

\tilde and \hat have wide versions that allow you to accent an expression: Symbol 	Command	Symbol 	Command \widehat{3+x}	\widehat{3+x}	\widetilde{abc}	\widetilde{abc} Others Symbol	Command	Symbol	Command	Symbol	Command \infty	\infty	\triangle	\triangle	\angle	\angle \aleph	\aleph	\hbar	\hbar	\imath	\imath \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.gif	\spadesuit	\Join	\Join	\blacksquare	\blacksquare \S	\S	\P	\P	\copyright	\copyright \pounds	\pounds 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 $$	\$	\&	\&	\%	\%	\#	\# \_	\_	\{	\{	\}	\}	\backslash	\backslash European Language Symbols Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command {\oe}	{\oe}	{\ae}	{\ae}	{\aa}	{\aa}	{\o}	{\o} {\OE}	{\OE}	{\AE}	{\AE}	{\AA}	{\AA}	{\O}	{\O} {\l}	{\l}	{\ss}	{\ss}	\text{!`}	!` {\L}	{\L}	{\SS}	{\SS}	\text{?`}	?` Bracketing Symbols

In mathematics, sometimes we need to enclose expressions in brackets or 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:

(\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

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

\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 Examples

x^y is the same as x^{y}, producing x^y. x_y is the same as x_{y}, producing x_y. However, x^10 is not the same as x^{10}. The former produces x^10 instead of x^{10}.

end
$$\lim_{x\to\infty}\frac{1}{x}$$

$$\lim_{n\to\infty}$$

$$\overrightarrow{a b}$$

$$\overleftarrow{c d}$$

$$A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C$$