Latex common formula format

1 Basic format,Will numbered each formula

\begin{equation}\label{eq1-1}
    a=b+c
\end{equation}

$\begin{equation}\label{eq1-1} a=b+c \end{equation}$ （1-1）

2. Multiple formulas are columns, only one number

\begin{equation}\label{eq1-2}
\begin{split}
a=b+c  \\
d=e+f
\end{split}
\end{equation}

3. A plurality of formulas:Each number

\begin{align}
a & =b+c \\
d & =e+f
\end{align}

$\begin{align} a & =b+c \\ d & =e+f \end{align}$

4. Segmentation function

\begin{equation}
f(x)=\left\{
\ begin {array} {rcl}% RCL is the way to it, you can try ~
0 & {0 \le x < 1000}\\
1 & {1000 \le x < 2000}\\
-1 & {2000 \le x < 3000}\\
0 & {3000 \le x <  4500}
\end{array} \right.
\end{equation}

$f(x)=\left\{ \begin{array}{rcl} 0 & {0 \le x < 1000}\\ 1 & {1000 \le x < 2000}\\ -1 & {2000 \le x < 3000}\\ 0 & {3000 \le x < 4500} \end{array} \right.$

6. ... I think it is random

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