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在 2 列证明环境中对齐所有方程式但不对齐文本？

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在 2 列证明环境中对齐所有方程式但不对齐文本？

我需要你帮我想出一些窍门或技巧，将我的 MWE 包含在一个双列页面中，并带有证明环境，其数学对齐，并包含用于解释的文本。问题是，当我运行它时，它超出了列空间。我希望它包含在一个双列页面文档中。

\documentclass[12pt,a4paper]{article}
\usepackage[latin1]{inputenc}

\usepackage{multicol}% set this to 2 colomn
\setlength{\columnsep}{7mm}% set the space betw colomn 7mm

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[left=2.00cm, right=2.00cm, top=2.00cm, bottom=2.00cm]{geometry}

\usepackage{ulem}
\newcommand{\msout}[1]{\text{\sout{\ensuremath{#1}}}}

\newcommand{\numberthis}{\refstepcounter{equation}\tag{\arabic{equation}}}
\newcommand{\labeln}[1]{\numberthis\label{#1}}
\newcommand{\mathonehalf}{\ensuremath{\frac{1}{2}}}

\usepackage{blindtext}
\begin{document}
\begin{multicols}{2}
    \blindtext
    \blindtext
\begin{proof}
    \begin{align}
    \mu &= np \\
    &= \mathonehalf n;\\
    \sigma &= \sqrt{np\left(1-p\right)} \labeln{eq:sigma}\\
    &=  \mathonehalf \sqrt{n};\\
    Z &= \dfrac{X-\mu}{\sigma}\\
    &= \frac{X-\mathonehalf n}{\mathonehalf \sqrt{n}};\\
    \vartriangle Z&= \frac{\left(X+1\right)-\mathonehalf n}{\mathonehalf 
        \sqrt{n}} - \frac{X-\mathonehalf n}{\mathonehalf \sqrt{n}}\\
    \vartriangle Z&= \dfrac{1}{\mathonehalf \sqrt{n}} \labeln{eq:dz}\\
    \lim_{n \to \infty} \vartriangle Z &= 0 \labeln{eq:limdz}\\
    \vartriangle Y&= \dfrac{n!}{\left(n-X-1\right)!\,X+1!}\left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right) - \dfrac{n!}{\left(n-X\right)!\,X!}\left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right) \nonumber\\
    &= \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right)n!\,\left[\dfrac{\left(n-x\right)!\,x!-\left(n-x-1\right)!\left(n-x\right)!}{\left(n-x-1\right)!\left(n-x\right)!\,\left(n-x\right)!\,x!}\right] \nonumber\\
    &= \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right)n!\,\left[\dfrac{\msout{\mathsf{\left(n-x-1\right)!\,x!}}\left[\left(n-x\right)-\left(x+1\right)\right]}{\msout{\mathsf{\left(n-x-1\right)!}}\left(x+1\right)!\,\left(n-x\right)!\,\msout{\mathsf{x!}}}\right] \nonumber\\
    &= \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right)\left[\dfrac{n!}{\left(x+1\right)!\,\left(n-x\right)!}\right]\left[\left(n-x\right)-\left(x+1\right)\right] \nonumber\\
    &= \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right)\left[\dfrac{n!}{\left(n-x\right)!\,x!}\right]\dfrac{\left(n-x-x-1\right)}{\left(x+1\right)} \nonumber\\
    \text{From equation \ref{eq:dz} and equation \eqref{eq:sigma} }\\
    \end{align} 
\end{proof}

References to $\sigma$ \eqref{eq:sigma} and $\Delta Z$ \eqref{eq:dz}.
\blindtext
\end{multicols}
\end{document}

答案1

您可以使用\intertext文本。除此之外，您可以overfull \hbox通过不对齐所有方程式并将右侧部分拆分为两行来摆脱 es。结果仍然不太吸引人，主要是因为您的表达式太大而无法放入如此狭窄的空间。

\documentclass[12pt,a4paper]{article}
\usepackage[latin1]{inputenc}

\usepackage{multicol}% set this to 2 colomn
\setlength{\columnsep}{7mm}% set the space betw colomn 7mm

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[left=2.00cm, right=2.00cm, top=2.00cm, bottom=2.00cm]{geometry}

\usepackage{ulem}
\newcommand{\msout}[1]{\text{\sout{\ensuremath{#1}}}}

\newcommand{\numberthis}{\refstepcounter{equation}\tag{\arabic{equation}}}
\newcommand{\labeln}[1]{\numberthis\label{#1}}
\newcommand{\mathonehalf}{\ensuremath{\frac{1}{2}}}

\usepackage{blindtext}
\begin{document}
\begin{multicols}{2}
    \blindtext
    \blindtext
\begin{proof}
    \begin{align}
    \mu =& np \\
    =& \mathonehalf n;\\
    \sigma =& \sqrt{np\left(1-p\right)} \labeln{eq:sigma}\\
    =&  \mathonehalf \sqrt{n};\\
    Z =& \dfrac{X-\mu}{\sigma}\\
    =& \frac{X-\mathonehalf n}{\mathonehalf \sqrt{n}};\\
    \vartriangle Z=& \frac{\left(X+1\right)-\mathonehalf n}{\mathonehalf 
        \sqrt{n}} - \frac{X-\mathonehalf n}{\mathonehalf \sqrt{n}}\\
    \vartriangle Z=& \dfrac{1}{\mathonehalf \sqrt{n}} \labeln{eq:dz}\\
    \lim_{n \to \infty} \vartriangle Z =& 0 \labeln{eq:limdz}
\end{align}
    \begin{align}
    \vartriangle Y=& \dfrac{n!}{\left(n-X-1\right)!\,X+1!}\left(\tfrac{1}{2}
    n\right)\left(\tfrac{1}{2} \sqrt{n}\right) \nonumber\\
    &\,- \dfrac{n!}{\left(n-X\right)!\,X!}\left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right) \nonumber\\
    =& \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right)n!\nonumber\\
    &\,\left[\dfrac{\left(n-x\right)!\,x!-\left(n-x-1\right)!\left(n-x\right)!}{\left(n-x-1\right)!\left(n-x\right)!\,\left(n-x\right)!\,x!}\right] \nonumber\\
    =& \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2}
    \sqrt{n}\right)n!\nonumber\\
    &\,\left[\dfrac{\msout{\mathsf{\left(n-x-1\right)!\,x!}}\left[\left(n-x\right)-\left(x+1\right)\right]}{\msout{\mathsf{\left(n-x-1\right)!}}\left(x+1\right)!\,\left(n-x\right)!\,\msout{\mathsf{x!}}}\right] \nonumber\\
    =& \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right)\left[\dfrac{n!}{\left(x+1\right)!\,\left(n-x\right)!}\right]
    \nonumber\\
    &\,\left[\left(n-x\right)-\left(x+1\right)\right] \nonumber\\
    =& \left(\tfrac{1}{2} n\right)\left(\tfrac{1}{2} \sqrt{n}\right)
    \left[\dfrac{n!}{\left(n-x\right)!\,x!}\right]\nonumber\\
    &\,\dfrac{\left(n-x-x-1\right)}{\left(x+1\right)} \nonumber\\
    \intertext{From equation \ref{eq:dz} and equation \eqref{eq:sigma} }\\
    \end{align} 
\end{proof}

References to $\sigma$ \eqref{eq:sigma} and $\Delta Z$ \eqref{eq:dz}.
\blindtext
\end{multicols}
\end{document}

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