latex中 用\begin{equation*}去掉编号为什么提示错误

关于x的不等式组 left{ begin{array}{l} {x＞m-1} \ {x＞m+2} end{array}right.的解集是x＞

英语翻译
∴$left{begin{array}{l}{1-2{k}^{2}≠0}\{△={16k}^{2}+16（{1-2k}^{2}）=16（1-{k}^{2}）;＞0}end{array}right.$
解得：-1＜k＜1且k≠±$frac{sqrt{2}}{2}$．
（2）设A（x1,y1）,B（x2,y2）,则x1+x2=$frac{4k}{1-2k^{2}}$
设P为AB中点,则P（$frac{x_{1}+x_{2}}{2}$,$frac{k（x_{1}+x_{2}）}{2}$+1）,即P（$frac{2k}{1-2k^{2}}$,$frac{1}{1-2k^{2}}$）,
∵M（3,0）到A、B两点的距离相等,
∴MP⊥AB,∴KMP•KAB=-1,
即k•$frac{frac{1}{{1-2k}^{2}}}{frac{2k}{{1-2k}^{2}}-3}$=-1,解得k=$frac{1}{2}$,或k=-1（舍去）,
∴k=$frac{1}{2}$．

ctex问题
源文件如下
documentclass[a4paper,12pt]{article}
begin{document}
ldots when Einstein introduced his formula
begin{equation} label{1}
e = m cdot c^2 ;,
end{equation}
which is at the same time the most widely known and
the least well understood physical formula
end{document}
请问公式后面;有什么用?