One 、 Formula writing

 From URL 
https://www.cnblogs.com/liangjianli/p/11616067.html
 It's best to write 
 stay word Copy and paste the formula in medium size 

 In line formula 
$ f(x) $
 The formula between lines 
$$ f(x) $$

 Numbered 
$$ a^2 + b^2 = c^2 \tag{
    no.1} $$
 auto number 
\begin{
    equation}
    a^2 + b^2 = c^2
\end{
    equation}

 Labels and numbers 
\begin{
    equation}\label{
    eq2}
    a^2 + b^2 = c^2
\end{
    equation}
 This is the first (\ref{
    eq2}) A formula 

 Automatically align and number separately  \\\\ escape \\ Line break 
\begin{
    align}
    x +  y = 1\\\\
    2x + y \neq 1\\\\
    3x +4y \leq 2\\\\
    4x \geq y
\end{
    align}

 Line feed 
\begin{
    equation}
    \begin{
    split}
        (x + y)(x + 4y) & = x^2 + 4xy + xy + 4y^2\\\\
                & = x^2 +5xy + 4y^2
    \end{
    split}
\end{
    equation}

 Line feed use &
 Control all alignment here 

 Category input 
\begin{
    equation}
    a_{
    i1}A_{
    j1} + a_{
    i2}A_{
    j2} + \cdots + a_{
    in}A_{
    jn} = 
    \begin{
    cases}
        \begin{
    vmatrix}A\end{
    vmatrix},& i =j\\\\
        0, & i \neq j
    \end{
    cases}
\end{
    equation}

Two 、 Ellipsis

\cdots It's a horizontal ellipsis 
\vdots It's a vertical ellipsis 
\ddots It's an ellipsis in the diagonal direction 
\ldots  Is an ellipsis aligned with the bottom line of the text 

3、 ... and 、 Curly braces

 label 
\big,\Big,\bigg,\Bigg
 for example  \big \{
    
 Single brace 
\left\{
    \right.
 If there is a left, there must be a right 

Four 、 And or not

∧
$\land$

∨
$\vee$

¬
$\neg$