为什么这个脚注显示了四次？

Question

这是我的代码：

\documentclass{beamer}
\begin{document}

\begin{frame}
\begin{definition}[Clopen Set]
 $A$ is a clopen set iff
    \begin{equation*}
        A \in \mathcal{A}\&\neg A \in \mathcal{A}\text{\footnote{Equivalently, $A \in\mathcal{A} \cap \neg \mathcal{A}$}}
    \end{equation*}         
\end{definition}
\end{frame}
    
\end{document}

但是，幻灯片看起来是这样的：

请帮忙 ：（

Answer 1

这样，它只出现一次：

\documentclass{beamer}
\begin{document}
    
    \begin{frame}
        \begin{definition}[Clopen Set]
            $A$ is a clopen set iff
            \begin{equation*}
                A \in \mathcal{A}\&\neg A \in \mathcal{A}\footnote{\text{Equivalently, $A \in\mathcal{A} \cap \neg \mathcal{A}$}}
            \end{equation*}         
        \end{definition}
    \end{frame}
    
\end{document}

Answer 2

没有理由使用\text，无论在\footnote其周围还是内部。

\documentclass{beamer}
\begin{document}

\begin{frame}
\begin{definition}[Clopen Set]
 $A$ is a clopen set iff
    \begin{equation*}
        A \in \mathcal{A}\mathrel{\&}\neg A \in \mathcal{A}
        \footnote{Equivalently, $A \in\mathcal{A} \cap \neg \mathcal{A}$}
    \end{equation*}
\end{definition}
\end{frame}

\end{document}

请注意\mathrel{\&}以获得更好的间距。

但为什么要加脚注呢？

\documentclass{beamer}
\begin{document}

\begin{frame}
\begin{definition}[Clopen Set]
 $A$ is a clopen set iff
    \begin{equation*}
        A \in \mathcal{A}\mathrel{\&}\neg A \in \mathcal{A}
        \footnote{Equivalently, $A \in\mathcal{A} \cap \neg \mathcal{A}$}
    \end{equation*}
\end{definition}
\end{frame}

\begin{frame}
\begin{definition}[Clopen Set]
 $A$ is a clopen set iff
    \begin{equation*}
        A \in \mathcal{A}\mathrel{\&}\neg A \in \mathcal{A}
    \end{equation*}
Equivalently, $A \in\mathcal{A} \cap \neg \mathcal{A}$
\end{definition}
\end{frame}

\end{document}

Answer 3

只是为了好玩：

\documentclass{beamer}
\begin{document}

\begin{frame}
\begin{definition}[Clopen Set]
 $A$ is a clopen set iff
    \begin{equation}
        A \in \mathcal{A}\&\neg A \in \mathcal{A}\tag*{\footnote{Equivalently, $A \in\mathcal{A} \cap \neg \mathcal{A}$}}
    \end{equation}
 or
    \begin{equation}
        A \in \mathcal{A}\&\neg A \in \mathcal{A}\tag*{Equivalently, $A \in\mathcal{A} \cap \neg \mathcal{A}$}
    \end{equation} 
 or
    \begin{align*}
        A \in \mathcal{A}\&\neg A \in \mathcal{A} && \text{Equivalently, } A \in\mathcal{A} \cap \neg \mathcal{A}
    \end{align*} 
\end{definition}
\end{frame}
    
\end{document}