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2020084.lyx
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\begin_layout Title
2020084号草稿
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数学主义
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前言
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我本来想为同学们写一份笔记来着。但现在我觉得没法写：一，我的数学水平很有限；二，“同学们”对于我来说还是个抽象的概念、模糊不清；三，我觉得笔记终究是个性化的内容
，因各人知识储备、学习目的、思维习惯不同而有不同的需求。我希望同学们都能写写笔记且互相分享、参考。
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本文档源代码托管于
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https://gitee.com/mathist/math2020084
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华东师大数学分析
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本章内容大致是为我们的数学分析课程所写的笔记.
因此, 如无上下文指明, 则``书''就是指华东师大数学分析第五版.
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符号表
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</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\mathbb{R}_{+}$
\end_inset
或
\begin_inset Formula $\mathbf{R}^{+}$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
全体正实数构成的集合
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $f_{n}\rightrightarrows f$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
一致收敛
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\sup S$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
数集
\begin_inset Formula $S$
\end_inset
的上确界
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $U(a;\delta)$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $a$
\end_inset
的
\begin_inset Formula $\delta$
\end_inset
邻域
\begin_inset Formula $(a-\delta,a+\delta)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $U^{\circ}(a;\delta)$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $a$
\end_inset
的空心
\begin_inset Formula $\delta$
\end_inset
邻域
\begin_inset Formula $(a-\delta,a)\cup(a,a+\delta)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $U_{+}(a;\delta)$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $a$
\end_inset
的
\begin_inset Formula $\delta$
\end_inset
右邻域
\begin_inset Formula $U_{+}(a;\delta)=[a,a+\delta)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $U_{-}(a;\delta)$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $a$
\end_inset
的
\begin_inset Formula $\delta$
\end_inset
左邻域
\begin_inset Formula $U_{-}(a,\delta)=(a-\delta,a]$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $U(\infty)$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\infty$
\end_inset
邻域
\begin_inset Formula $(-\infty,M)\cup(M,+\infty)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $U(+\infty)$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $+\infty$
\end_inset
邻域
\begin_inset Formula $(M,+\infty)$
\end_inset
\end_layout
\end_inset
</cell>
</row>