关于第一次使用latex写文章

一次简单的latex公式输出

整体的代码

\usepackage{amsmath, bookmark,amsthm, amssymb, graphicx}
\usepackage{ctex}
\usepackage{geometry}
\geometry{a4paper, scale=0.9}
\title{Homework2}
\author{xxx}
\date{\today}
\begin{document}
\maketitle
\section{Q:}
Let $\mathcal{F}_i$ be a $\sigma-field$ ,i=1,2 ……
，$\mathcal{F}=\bigcap\limits_{i=1}^\infty \mathcal{F}_i $,
then $\mathcal{F}$ is a $\sigma-field $.
\section{Proof:}
For any i ,we know that $\varOmega\subset\mathcal{F}_i $,so $\varOmega\subset\bigcap\limits_{i=1}
^\infty\mathcal{F}_i$.Then $
\varOmega\subset\mathcal{F}$.Next,we can let any $\mathbf{A}\subset\mathcal{F}$,
so $\mathbf{A}\subset\mathcal{F}_i $,
so $\varOmega \backslash \mathbf{A}\subset\mathcal{F}_i$For any i,$\varOmega \backslash \mathbf{A}\subset\mathcal{F}_i$so,$\varOmega \backslash \mathbf{A}\subset\bigcap\limits_{i=1}^\infty\mathcal{F}_i$so,$\varOmega \backslash \mathbf{A}\subset\mathcal{F}$we can get $\{\mathbf{A}_n\}_{i=1}^\infty
\subseteq\mathcal{F}_i $
,so $\mathbf{A}_n\subseteq\mathcal{F}_i$For $\mathcal{F}_i$ is $\sigma -field$ ,
so $\bigcup\limits_{i=1}^\infty\mathbf{A}\subseteq
\mathcal{F}_i$so $\bigcup\limits_{i=1}^\infty\mathbf{A}\subseteq\bigcap\limits_{i=1}^\infty\mathcal{F}_i=\mathcal{F}$so $\mathcal{F}$is a $\sigma-field$
\end{document}```