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让不平等变得整洁

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让不平等变得整洁

如何使不等式变得整齐？我发现所有<符号之间的水平间距都太可怕了。我对 造成的垂直扭曲也有同样的感觉\cfrac。

Suppose $\delta < \cfrac{1}{2}$ 
\begin{equation*}
\begin{split}
    |x| < \sqrt{\epsilon} < \cfrac{1}{2} & \Rightarrow |x^2| < \epsilon < \cfrac{1}{4} \\
    & \Rightarrow |-x^2| < \epsilon < \cfrac{1}{4}  \\
    & \Rightarrow - \cfrac{1}{4} < -\epsilon < -x^2 < \epsilon < \cfrac{1}{4} \\
    & \Rightarrow \cfrac{3}{4} < 1 - x^2 < \epsilon + 1 < \cfrac{5}{4} \\
    & \Rightarrow  \sqrt{1-x^2} < \sqrt{\epsilon + 1} < \epsilon + 1\\ 
    & \Rightarrow |\sqrt{1-x^2}| < \sqrt{\epsilon + 1} < \epsilon +1 \\
    |x| < \sqrt{\epsilon} < \cfrac{1}{2} &\Rightarrow |\sqrt{1-x^2}| < \epsilon + 1
\end{split}
\end{equation*}

答案1

我可能会这样做：

\documentclass[a4paper]{memoir} %just because that is the default class in my editor
\usepackage{mathtools}
\DeclarePairedDelimiter\abs\lvert\rvert
\begin{document}
Suppose $\delta < \frac{1}{2}$ 
\begin{equation*}
  \begin{alignedat}{2}
    && \abs{x} &< \sqrt{\epsilon} < \tfrac{1}{2}
    \\
    & \Rightarrow \quad&\abs{x^2} &< \epsilon < \tfrac{1}{4}
    \\
    & \Rightarrow &\abs{-x^2} &< \epsilon < \tfrac{1}{4}
    \\
    & \Rightarrow &- \tfrac{1}{4} &< -\epsilon < -x^2 < \epsilon <
    \tfrac{1}{4}
    \\
    & \Rightarrow &\tfrac{3}{4} &< 1 - x^2 < \epsilon + 1 < \tfrac{5}{4}
    \\
    & \Rightarrow &\sqrt{1-x^2} &< \sqrt{\epsilon + 1} < \epsilon + 1
    \\
    & \Rightarrow &\abs{\sqrt{1-x^2}} &< \sqrt{\epsilon + 1} < \epsilon
    +1
    \\
    && \abs{x} &< \sqrt{\epsilon} < \tfrac{1}{2}
    \\
    &\Rightarrow & \abs{\sqrt{1-x^2}} &< \epsilon + 1
  \end{alignedat}
\end{equation*}
\end{document}

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