MathJax basic tutorial and quick reference(MathJax教程)

Basics

• For inline formulas, enclose the formula in $...$. For displayed formulas, use $$...$$.
  These render differently. For example, type$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$ to show $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$ (which is inline mode) or type $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$ to show

\[\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\]

(which is display mode).

• For Greek letters, use \alpha, \beta, …, \omega : $\alpha, \beta, \ldots, \omega$ . For uppercase, use \Gamma, \Delta, …, \Omega : $\Gamma, \Delta, \ldots, \Omega$ . Some Greek letters have variant forms: \epsilon \varepsilon $\epsilon, \varepsilon$ , \phi \varphi $\phi, \varphi$ , and others.

• For superscripts and subscripts, use ^ and _. For example, x_i^2: $x_i^2$ , \log_2 x: $\log_2 x$ .

• Groups. Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {…}. If you do 10^10, you will get a surprise: $10^10$ . But 10^{10} gives what you probably wanted: $10^{10}$ . Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is ${x^y}^z$, and x^{y^z} is $x^{y^z}$ . Observe the difference between x_i^2 $x_i^2$ and x_{i^2} $x_{i^2}$.

• Parentheses Ordinary symbols ()[] make parentheses and brackets $(2+3)[4+4]$. Use \{ and \} for curly braces ${}$.
  These do bot scale with the formula in between, so if you write (\frac{\sqrt x}{y^3}) the parentheses will be too small: $(\frac{\sqrt x}{y^3})$ . Using \left(…\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac{\sqrt x}{y^3}\right) is $\left(\frac{\sqrt x}{y^3}\right)$ .
  \left and \right apply to all the following sorts of parentheses: ( and ) $\left( x \right)$ , [ and ] $\left[ x \right]$ , \{ and \} $\left\lbrace x \right\rbrace$ , | $\left| x \right|$ , \vert $\left\vert x \right\vert$ , \Vert $\left\Vert x \right\Vert$ , \langle and \rangle $\left\langle x \right\rangle$ , \lceil and \rceil $\left\lceil x \right\rceil$ , and \lfloor and \rfloor $\left\lfloor x \right\rfloor$ . \middle can be used to add additional dividers. There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is $\left.\frac12\right\rbrace$ .
  If manual size adjustment are required: \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) gives $\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)$ .

• Sums and integrals \sum and \int; the subscript is the lower limit and the superscript is the upper limit, so for example \sum_1^n $\sum_1^n$ . Don’t forget {…} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is $\sum_{i=0}^\infty i^2$ . Similarly, \prod $\prod$ , \int $\int$ , \bigcup $\bigcup$ , \bigcap $\bigcap$, \iint $\iint$, \iiint $\iiint$, \idotsint $\idotsint$.

• Fractions There are three ways to make these. \frac ab applies to the next two groups, and produces $\frac ab$ ; for more complicated numerators and denominators use {…}: \frac{a+1}{b+1} is $\frac{a+1}{b+1}$ . If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in: {a+1\over b+1} is ${a+1\over b+1}$ . Using \cfrac{a}{b} command is useful for continued fractions $\cfrac{a}{b}$.

• Fonts
  • Use mathbb or Bbb for “blackboard bold”: $\mathbb{ABCDEFGHIJK}$ , $\mathbb{abcdefghijk}$ .
  • Use mathbf for boldface: $\mathbf{ABCDEFGHIJK}$,$\mathbf{abcdefghijk}$
    • For expression based characters, use \boldsymbol instead: $\boldsymbol \alpha$ .
  • Use \mathit for italics: $\mathit{ABCDEFGHIJK}$, $\mathit{abcdefghijk}$ .
  • Use \pmb for boldfaces italics: $\pmb{ABCDEFGHIJK}$, $\pmb{abcdefghijk}$ .
  • Use \mathtt for “typewriter” font: $\mathtt{ABCDEFGHIJK}$, $\mathtt{abcdefghijk}$ .
  • Use \mathrm for roman font: $\mathrm{ABCDEFGHIJK}$ , $\mathrm{abcdefghijk}$ .
  • Use \mathsf for sans-serif font: $\mathsf{ABCDEFGHIJK}$ , $\mathsf{abcdefghijk}$ .
  • Use \mathcal for “calligraphic” letters: $\mathcal{ABCDEFGHIJK}$ , $\mathcal{abcdefghijk}$ .
  • Use \mathscr for script letters: $\mathscr{ABCDEFGHIJK}$ , $\mathscr{abcdefghijk}$ .
  • Use \mathfrak for “Fraktur” (old German style) letters: $\mathfrak{ABCDEFGHIJK}$ , $\mathfrak{abcdefghijk}$ .

• Radical signs / roots Use \sqrt, which adjusts to the size of its argument: \sqrt{x^3} $\sqrt{x^3}$ ; \sqrt[3]{\frac xy} $\sqrt[3]{\frac xy}$ . For complicated expressions, consider using {...}^{1/2}instead.

• Some special functions such as “lim”, “sin”, “max”, “ln”, and so on are normally set in roman font instead of italic font. Use \lim, \sin, etc. to make these: \sin x $\sin x$, not sin x $sin x$. Use subscripts to attach a notation to \lim: \lim_{x\to 0}

\[\lim_{x\to 0}\]

Nonstandard function names can be set with \operatorname{foo}(x) $\operatorname{foo}(x)$ .

• There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:
  • \lt \gt \le \leq \leqq \leqslant \ge \geq \geqq \geqslant \neq $\lt, \gt, \le, \leq, \leqq, \leqslant, \ge, \geq, \geqq, \geqslant, \neq$ . You can use \not to put a slash through almost anything: \not\lt $\not\lt$ but it often looks bad.
  • \times \div \pm \mp $\times, \div, \pm, \mp$ . \cdot is a centered dot: $x \cdot y$
  • \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing $\cup, \cap, \setminus, \subset, \subseteq, \subsetneq, \supset, \in, \notin, \emptyset, \varnothing $
  • {n+1 \choose 2k} or \binom{n+1}{2k} $\binom{n+1}{2k}$
  • \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto $\to, \rightarrow, \leftarrow, \Rightarrow, \Leftarrow, \mapsto$
  • \land \lor \lnot \forall \exists \top \bot \vdash \vDash $\land, \lor, \lnot, \forall, \exists, \top, \bot, \vdash, \vDash$
  • \star \ast \oplus \circ \bullet $\star, \ast, \oplus, \circ, \bullet$
  • \approx \sim \simeq \cong \equiv \prec \lhd \therefore $\approx, \sim, \simeq, \cong, \equiv, \prec, \lhd, \therefore$
  • \infty \aleph_0 $\infty \aleph_0$ , \nabla \partial $\nabla \partial$ , \Im \Re $\Im \Re$
  • For modular equivalence, use \pmod like this: a\equiv b\pmod n $a\equiv b\pmod n$ .
  • For the binary mod operator, use \bmod like this: `a\bmod 17$.
  • \ldots in the dots in $a_1, a_2, \ldots, a_n$ \cdots in the dots in $a_1 + a_2 + \cdots + a_n$
  • Script lowercase l is \ell $\ell$ .

  Detexify lets you draw a symbol on a web page and then lists the $\TeX$ symbols that seem to resemble it. These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains a list of currently supported $\LaTeX$ commands, and one can also check Dr. Carol JVF Burns’s page of $\TeX$ Commands Available in MathJax.

• Spaces MathJax usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJax puts in: a␣b and a␣␣␣␣b are both $ab$. To add more space, use \, for a thin space $a\,b$; \; for a wider space $a \; b$. \quad and \qquad are large spaces: $a \quad b$ , $a \qquad b$ .

  To set plain text, use \text{…}: $\lbrace x \in s \; | \; x \text{ is extra large}\rbrace$ . You can nest $…$ inside of \text{…}, for example to access spaces.

• Accents and diacritical marks Use \hat for a single symbol $\hat x$ , \widehat for a larger formula $\widehat{xy}$ . If you make it too wide, it will look silly. Similarly, there are \bar $\bar x$ and \overline $\overline{xyz}$ , and \vec $\vec x$ and \overrightarrow $\overrightarrow{xy}$ and \overleftrightarrow $\overleftrightarrow{xy}$ . For dots, as in $\frac{d}{dx}x\dot x = {\dot x}^2 + x\dot x$ , use \dot and \ddot

• Special characters used for MathJax interpreting can be escaped using the \ character: \\\$ $\$$ , \{ $\lbrace$ , \\_ $\_$ , etc. If you want \ itself, you should use \backslash (symbol) or \setminus (binary operation) for $\backslash$ , because \\ is for a new line.

Tutorial ends here. And for more derail see Contents below.

Contents

Alphabetical list of links to To MathJax Topics, by title:

• Absolute values and norms • Additional symbolic decorations • Aligning Equations
• Alternative Ways of Writing in LaTeX • Annotations of reasoning • Arbitrary operators
• Arrays • Big braces • Colors
• Commutative diagrams • Continued fractions • Crossing things out
• Definitions by cases (piecewise functions) • Degree symbol • Display style
• Equation numbering • Fussy spacing issues • Highlighting expressions
• Left and right arrows • Limits • Linear programming
• Long division • Math Programming • Matrices
• Markov Chains • Mixing code and MathJax formatting on lines • The \newcommand function
• Numbering Equations • Overlaying Symbols • Packs of cards
• Symbols • System of equations • Tables
• Tags and references • Tensor indices • Units
• Vertical spacing

Matrix

• Use $$\begin{matrix}…\end{matrix}$$ In between the \begin and \end, put the matrix elements. End each matrix row with \\, and separate matrix elements with &. For example,

  $$
  \begin{matrix}
  1 & x & x^2 \\
  1 & y & y^2 \\
  1 & z & z^2 \\
  \end{matrix}
  $$
  

  produces:

\[\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}\]

MathJax will adjust the sizes of the rows and columns so that everything fits.

• To add brackets, either use \left…\right, or replace matrix with pmatrix \(\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}\) , bmatrix \(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\) , Bmatrix \(\begin{Bmatrix} 1 & 2 \\ 3 & 4 \end{Bmatrix}\) , vmatrix \(\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}\) , Vmatrix \(\begin{Vmatrix} 1 & 2 \\ 3 & 4 \end{Vmatrix}\).
• Use \cdots $\cdots$ \ddots $\ddots$ \vdots $\vdots$ when you want to omit some of the entries:

\[\begin{pmatrix} 1 & a_1 & a_1^2 & \cdots & a_1^n \\ 1 & a_2 & a_2^2 & \cdots & a_2^n \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & a_m & a_m^2 & \cdots & a_m^n \end{pmatrix}\]

• For horizontally “augmented” matrices, put parentheses or brackets around a suitably-formatted table; see Arrays below for details. Here is an example:

\[\left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array} \right]\]

is produced by:

$$ \left[
\begin{array}{cc|c}
  1&2&3\\
  4&5&6
\end{array}
\right] $$

The cc|c is the crucial part here; it says that there are three centered columns with a vertical bar between the second and third.

• For vertically “augmented” matrices, use \hline. For example

\[\begin{pmatrix} a & b\\ c & d\\ \hline 1 & 0\\ 0 & 1 \end{pmatrix}\]

is produced by:

$$
  \begin{pmatrix}
    a & b\\
    c & d\\
  \hline
    1 & 0\\
    0 & 1
  \end{pmatrix}
$$

• For small inline matrices use \bigl(\begin{smallmatrix} ... \end{smallmatrix}\bigr), e.g. \(\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)\) is produced by:

  $$\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$$
  

Symbols

In general, you have to search in long tables about a specific symbol you’re looking for, things like $\Psi, \delta, \zeta, \geq, \subseteq$ … And it turns out that this operation can be frustrating and time consuming, which can cause the buddy to abandon writing the complete $\LaTeX$ sentence in his answer, or in some cases, the complete answer itself.

That’s why the tool that I will present you in this post was conceived. Basically, it is a $\LaTeX$ handwritten symbol recognition. Example in image:

Here is the website: Detexify No more frustration.

Aligned equations

Often people want a series of equations where the equals signs are aligned. To get this, use \begin{align}…\end{align}. Each line should end with \\, and should contain an ampersand at the point to align at, typically immediately before the equals sign.

For example:

\[\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align}\]

is produced by

\begin{align}
\sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\
 & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ 
 & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
 & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ 
 & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}

The usual $$ marks that delimit the display may be omitted here.

Definitions by cases (piecewise functions)

Use \begin{cases}…\end{cases}. End each case with a \\, and use & before parts that should be aligned.

For example, you get this:

\[f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}\]

by writing this:

f(n) =
\begin{cases}
n/2,  & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}

The brace can be moved to the right:

\[\left. \begin{array}{l} \text{if $n$ is even:}&n/2\\ \text{if $n$ is odd:}&3n+1 \end{array} \right\} =f(n)\]

by writing this:

\left.
\begin{array}{l}
\text{if $n$ is even:}&n/2\\
\text{if $n$ is odd:}&3n+1
\end{array}
\right\}
=f(n)

To get a larger vertical space between cases we can use \\[2ex] instead of \\. For example, you get this:

\[f(n) = \begin{cases} \frac{n}{2}, & \text{if $n$ is even} \\[2ex] 3n+1, & \text{if $n$ is odd} \end{cases}\]

by writing this:

f(n) =
\begin{cases}
\frac{n}{2},  & \text{if $n$ is even} \\[2ex]
3n+1, & \text{if $n$ is odd}
\end{cases}

(An ‘ex’ is a length equal to the height of the letter x; 2ex here means the space should be two exes high.)

Arrays

It is often easier to read tables formatted in MathJax rather than plain text or a fixed width font. Arrays and tables are created with the array environment. Just after \begin{array}the format of each column should be listed, use c for a center aligned column, r for right aligned, l for left aligned and a | for a vertical line. Just as with matrices, cells are separated with & and rows are broken using \\. A horizontal line spanning the array can be placed before the current line with \hline.

For example,

\[\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}\]

is produced by:

\begin{array}{c|lcr}
n & \text{Left} & \text{Center} & \text{Right} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}

Arrays can be nested to make an array of tables.

For example,

\[\begin{array}{c} \begin{array}{cc} \begin{array}{c|cccc} \text{min} & 0 & 1 & 2 & 3\\ \hline 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 1\\ 2 & 0 & 1 & 2 & 2\\ 3 & 0 & 1 & 2 & 3 \end{array} & \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 \end{array} \end{array} \\ \begin{array}{c|cccc} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} \end{array}\]

As the source for the preceding array is long, please right-click on one of the tables and choose $\mathtt{Show \; Math \; As } ▸ \mathtt{Tex \; Commands}$ .

Fussy spacing issues

These are issues that won’t affect the correctness of formulas, but might make them look significantly better or worse. Beginners should feel free to ignore this advice; someone else will correct it for them, or more likely nobody will care.

Don’t use \frac in exponents or limits of integrals; it looks bad and can be confusing, which is why it is rarely done in professional mathematical typesetting. Write the fraction horizontally, with a slash:

\[\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}\]

The | symbol has the wrong spacing when it is used as a divider, for example in set comprehensions. Use \mid instead:

\[\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \{x|x^2\in\Bbb Z\} & \{x\mid x^2\in\Bbb Z\} \\ \end{array}\]

When using stretchable delimiters (i.e. with \left and \right), it may be preferable to use \,\middle|\,. This produces a stretchable vertical bar with a little bit of space around it. Another alternative is to use a colon instead.

\[\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \left\{\dfrac{m}{n} \mid m,n\in\Bbb Z\right\} & \left\{\dfrac{m}{n} \,\middle|\, m,n\in\Bbb Z\right\} \\ \end{array}\]

For double and triple integrals, don’t use \int\int or \int\int\int. Instead use the special forms \iint and \iiint:

\[\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \int\int_S f(x)\,dy\,dx & \iint_S f(x)\,dy\,dx \\ \int\int\int_V f(x)\,dz\,dy\,dx & \iiint_V f(x)\,dz\,dy\,dx \end{array}\]

Use \, to insert a thin space before differentials; without this $\TeX$ will mash them together:

\[\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \iiint_V f(x)dz dy dx & \iiint_V f(x)\,dz\,dy\,dx \end{array}\]

Crossing things out

Use \require{cancel} in the first formula in your post that requires cancelling; you need it only once per page. Then use:

\[\require{cancel}\begin{array}{rl} \verb|y+\cancel{x}| & y+\cancel{x}\\ \verb|\cancel{y+x}| & \cancel{y+x}\\ \verb|y+\bcancel{x}| & y+\bcancel{x}\\ \verb|y+\xcancel{x}| & y+\xcancel{x}\\ \verb|y+\cancelto{0}{x}| & y+\cancelto{0}{x}\\ \verb+\frac{1\cancel9}{\cancel95} = \frac15+& \frac{1\cancel9}{\cancel95} = \frac15 \\ \end{array}\]

Use \require{enclose} for the following:

\[\require{enclose}\begin{array}{rl} \verb|\enclose{horizontalstrike}{x+y}| & \enclose{horizontalstrike}{x+y}\\ \verb|\enclose{verticalstrike}{\frac xy}| & \enclose{verticalstrike}{\frac xy}\\ \verb|\enclose{updiagonalstrike}{x+y}| & \enclose{updiagonalstrike}{x+y}\\ \verb|\enclose{downdiagonalstrike}{x+y}| & \enclose{downdiagonalstrike}{x+y}\\ \verb|\enclose{horizontalstrike,updiagonalstrike}{x+y}| & \enclose{horizontalstrike,updiagonalstrike}{x+y}\\ \end{array}\]

\enclose can also produce enclosing boxes, circles, and other notations; see MathML menclose documentation for a complete list.

System of equations

• Use \begin{array}…\end{array} and \left\{…\right. For example, you get this:

\[\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.\]

by writing this:

\left\{ 
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\ 
a_2x+b_2y+c_2z=d_2 \\ 
a_3x+b_3y+c_3z=d_3
\end{array}
\right. 

• To align the = signs use \begin{aligned}...\end{aligned} and \left\{…\right. (see asmeurer’s comment)

\[\left\{ \begin{aligned} a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y&=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{aligned} \right.\]

whose code is

\left\{
\begin{aligned} 
a_1x+b_1y+c_1z &=d_1+e_1 \\ 
a_2x+b_2y&=d_2 \\ 
a_3x+b_3y+c_3z &=d_3 
\end{aligned} 
\right.

• To align the = signs and the terms as in

\[\left\{ \begin{array}{ll} a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y &=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{array} \right.\]

use array with l (for “align left”; there are also c and r) parameters

\left\{
\begin{array}{ll}
a_1x+b_1y+c_1z &=d_1+e_1 \\ 
a_2x+b_2y &=d_2 \\ 
a_3x+b_3y+c_3z &=d_3 
\end{array} 
\right.

• Vertical space between equations. As explained in Definitions by cases to get a larger vertical space between equations we can use \\[2ex] instead of \\. The system

\[\begin{cases} a_1x+b_1y+c_1z=d_1 \\[2ex] a_2x+b_2y+c_2z=d_2 \\[2ex] a_3x+b_3y+c_3z=d_3 \end{cases}\]

is generated by the following code

\begin{cases}
a_1x+b_1y+c_1z=d_1 \\[2ex] 
a_2x+b_2y+c_2z=d_2 \\[2ex] 
a_3x+b_3y+c_3z=d_3
\end{cases}

in comparison with

\[\begin{cases} a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\ a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\ a_3x+b_3y+c_3z=\frac{p_3}{q_3} \end{cases}\]

whose code is:

\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}

• In response to elect's comment. The following code

\left\{ 
\begin{array}{l}
0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\[2ex] 
0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} 
\end{array}
\right.

produces

\[\left\{ \begin{array}{l} 0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\[2ex] 0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right.\]

Colors

Named colors are browser-dependent; if a browser doesn’t know a particular color name, it may render the text as black. The following colors are standard in HTML4 and CSS2 and should be interpreted the same by most browsers:

\[\begin{array}{|rc|} \hline \verb+\color{black}{text}+ & \color{black}{text} \\ \verb+\color{gray}{text}+ & \color{gray}{text} \\ \verb+\color{silver}{text}+ & \color{silver}{text} \\ \verb+\color{white}{text}+ & \color{white}{text} \\ \hline \verb+\color{maroon}{text}+ & \color{maroon}{text} \\ \verb+\color{red}{text}+ & \color{red}{text} \\ \verb+\color{yellow}{text}+ & \color{yellow}{text} \\ \verb+\color{lime}{text}+ & \color{lime}{text} \\ \verb+\color{olive}{text}+ & \color{olive}{text} \\ \verb+\color{green}{text}+ & \color{green}{text} \\ \verb+\color{teal}{text}+ & \color{teal}{text} \\ \verb+\color{aqua}{text}+ & \color{aqua}{text} \\ \verb+\color{blue}{text}+ & \color{blue}{text} \\ \verb+\color{navy}{text}+ & \color{navy}{text} \\ \verb+\color{purple}{text}+ & \color{purple}{text} \\ \verb+\color{fuchsia}{text}+ & \color{magenta}{text} \\ \hline \end{array}\]

HTML5 and CSS 3 define an additional 124 color names that will be supported on many browsers.

Math Stack Exchange’s default style uses a light-colored page background, so avoid using light colors for text. Stick to darker colors like maroon, green, blue, and purple, and remember also that 7–10% of men are color-blind and have difficulty distinguishing red and green.

The color may also have the form #rgb where 𝑟,𝑔,𝑏 are in the range or 0–9, a–f and represent the intensity of red, green, and blue on a scale of 0–15, with a=10, b=11, … f=15. For example:

\[\begin{array}{|rrrrrrrr|}\hline \verb+#000+ & \color{#000}{text} & & & \verb+#00F+ & \color{#00F}{text} & & \\ & & \verb+#0F0+ & \color{#0F0}{text} & & & \verb+#0FF+ & \color{#0FF}{text}\\ \verb+#F00+ & \color{#F00}{text} & & & \verb+#F0F+ & \color{#F0F}{text} & & \\ & & \verb+#FF0+ & \color{#FF0}{text} & & & \verb+#FFF+ & \color{#FFF}{text}\\ \hline \end{array}\] \[\begin{array}{|rrrrrrrr|} \hline \verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text} \\ \verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text} \\ \verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text} \\ \verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text} \\ \hline \verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text} \\ \verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text} \\ \verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text} \\ \verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text} \\ \hline \verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text} \\ \verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text} \\ \verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text} \\ \verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text} \\ \hline \end{array}\]

You can have a look here for quick reference on colors in HTML.

Additional symbolic decorations

To see Tex Commands right click on the Math

\overline: $\overline{A} \; \overline{AA} \; \overline{AAA}$

\underline: $\underline{B} \; \underline{BB} \; \underline{BBB}$

\widetilde: $\widetilde{C} \; \widetilde{CC} \; \widetilde{CCC}$

\widehat: $\widehat{D} \; \widehat{DD} \; \widehat{DDD}$

\fbox: $\fbox{E} \; \fbox{EE} \; \fbox{EEE}$

\underleftarrow: $\underleftarrow{F} \; \underleftarrow{FF} \; \underleftarrow{FFF} \qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\underrightarrow{G} \; \underrightarrow{GG} \; \underrightarrow{GGG} \qquad$ variant: \xleftarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\underleftrightarrow{H} \; \underleftrightarrow{HH} \; \underleftrightarrow{HHH}$

\overrightarrow: $\overrightarrow{AB} \; \overrightarrow{ABAB} \; \overrightarrow{ABABAB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is

\[\underbrace{a\cdot a\cdots a}_{b\text{ times}}\]

Note: \varliminf: $\varliminf$ and \varlimsup: $\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check I$

\acute: $\acute J$

\grave: $\grave K$

\vec: $\vec{u} \; \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x , \ddot x, \dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{level}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

\underset{below}{level}: $\underset{@}{ABC}\ \underset{x^2}{\longmapsto}\ \underset{\bullet\circ\circ\bullet}{T}$

You can use these together too. You can type $X\overset{a}{\underset{b}{\to}}Y$ with X\overset{a}{\underset{b}{\to}}Y.

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ .

Commutative diagrams

AMScd diagrams must start with a “require”:

\require{AMScd}
\begin{CD}
A @>a>> B\\
@V b V V= @VV c V\\
C @>>d> D
\end{CD}

get this diagram:

\[\require{AMScd} \begin{CD} A @>a>> B\\ @V b V V= @VV c V\\ C @>>d> D \end{CD}\]

@>>> is used for arrow right

@<<< is used for arrow left

@VVV is used for arrow down

@AAA is used for arrow up

@= is used for horizontal double line

@| is used for vertical double line

@. is used for no arrow

Another example:

\require{AMScd}
\begin{CD}
    A @>>> B @>{\text{very long label}}>> C \\
    @. @AAA @| \\
    D @= E @<<< F
\end{CD}

\[\require{AMScd} \begin{CD} A @>>> B @>{\text{very long label}}>> C \\ @. @AAA @| \\ D @= E @<<< F \end{CD}\]

Long labels increase the length of the arrow and in this version also automatically increase corresponding arrows.

\require{AMScd}
\begin{CD}
  RCOHR'SO_3Na @>{\text{Hydrolysis,$\Delta, Dil.HCl$}}>> (RCOR')+NaCl+SO_2+ H_2O
\end{CD}

\[\require{AMScd} \begin{CD} \text{RCOHR'SO$_3$Na} @>{\text{Hydrolysis, $\Delta,$ Dil. HCl}}>> \text{(RCOR')+NaCl+SO$_2$+ H$_2$O} \end{CD}\]

Continued fractions

https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference