latex中的math

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
E = mc^2
\end{equation}
\[ E = mc^2 \]
\[ \boxed{E = mc^2} \]

\[x_{xj}^2\quad \sqrt[2]{x}\]

$\frac{1}{2} \dfrac{1}{2}$
\[\frac{1}{2} \tfrac{1}{2}\]

\[\pm \times \div \cdot \cap \cup \geq \leq \neq \approx \equiv\]

$\sum_{i=1}^n i \prod_{i=1}^n \lim_{x\to0}x^2 \int_a^b x^2 dx$
\[\sum_{i=1}^n i \prod_{i=1}^n \lim_{x\to0}x^2 \int_a^b x^2 dx\]

\[\iint \iiint \iiiint\]

\[\xleftarrow{x + y + z}\quad
\xrightarrow[x < y]{a * b * c}\]

\[\begin{array}{ccc}
x_1 & x_2 & \dots \\
x_3 & x_4 & \dots \\
\vdots & \vdots & \ddots \\
\end{array}\]

\begin {multline}
x=a+b+c+\\
d+e+f+g
\end{multline}

\[ \begin{split}
x=&a+b+c+\\
&d+e+f+g
\end{split}
\]

\begin{gather}
a=b+c+d\\
x=y+z
\end{gather}

\begin{align}
a&=b+c+d\\
x&=y+z
\end{align}

\[ y=\begin{cases}
-x & x<0\\
x & x\geq0
\end{cases}
\]

\newtheorem{defination}{defination}[section]
\newtheorem{theorem}{theorem}[section]
\newtheorem{lemma}[theorem]{lemma}
\newtheorem{corollary}[theorem]{corollary}

\begin{defination}
Java is good
\end{defination}

\begin{theorem}
Java is good
\end{theorem}

\begin{lemma}
Java is good
\end{lemma}

\begin{corollary}
Java is good
\end{corollary}

\end{document}