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Add hyperref linking and fix other refs.

finite-set-exercises
Joshua Potter 2023-07-12 10:54:35 -06:00
parent 5991554fcb
commit e3205a1e5d
5 changed files with 409 additions and 406 deletions
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316
Bookshelf/Apostol.tex
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6
Bookshelf/Enderton/Logic.tex
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@ -13,7 +13,7 @@
\renewcommand\thechapter{R} \renewcommand\thechapter{R}
\chapter{Reference}% \chapter{Reference}%
\label{chap:reference} \hyperlabel{chap:reference}
\endgroup \endgroup
@ -21,10 +21,10 @@
\setcounter{chapter}{0} \setcounter{chapter}{0}
\addtocounter{chapter}{-1} \addtocounter{chapter}{-1}
\chapter{Useful Facts About Sets}% \chapter{Useful Facts About Sets}%
\label{chap:useful-facts-about-sets} \hyperlabel{chap:useful-facts-about-sets}
\section{\sorry{Lemma 0A}}% \section{\sorry{Lemma 0A}}%
\label{sec:lemma-0a} \hyperlabel{sec:lemma-0a}
Assume that $\langle x_1, \ldots, x_m \rangle = Assume that $\langle x_1, \ldots, x_m \rangle =
\langle y_1, \ldots, y_m, \ldots, y_{m+k} \rangle$. \langle y_1, \ldots, y_m, \ldots, y_{m+k} \rangle$.

476
Bookshelf/Enderton/Set.tex
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14
Common/Real/Sequence.tex
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@ -10,15 +10,15 @@
\tableofcontents \tableofcontents
\section{Summations}% \section{Summations}%
\label{sec:summations} \hyperlabel{sec:summations}
\subsection{\verified{Arithmetic Series}}% \subsection{\verified{Arithmetic Series}}%
\label{sub:sum-arithmetic-series} \hyperlabel{sub:sum-arithmetic-series}
Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$. Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
Then for some $n \in \mathbb{N}$, Then for some $n \in \mathbb{N}$,
\begin{equation} \begin{equation}
\label{sub:sum-arithmetic-series-eq1} \hyperlabel{sub:sum-arithmetic-series-eq1}
\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}. \sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.
\end{equation} \end{equation}
@ -30,7 +30,7 @@ Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$. Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
By definition, for all $k \in \mathbb{N}$, By definition, for all $k \in \mathbb{N}$,
\begin{equation} \begin{equation}
\label{sub:sum-arithmetic-series-eq2} \hyperlabel{sub:sum-arithmetic-series-eq2}
a_k = (a_0 + kd). a_k = (a_0 + kd).
\end{equation} \end{equation}
Define predicate $P(n)$ as "identity \eqref{sub:sum-arithmetic-series-eq1} Define predicate $P(n)$ as "identity \eqref{sub:sum-arithmetic-series-eq1}
@ -73,12 +73,12 @@ Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
\end{proof} \end{proof}
\subsection{\verified{Geometric Series}}% \subsection{\verified{Geometric Series}}%
\label{sub:sum-geometric-series} \hyperlabel{sub:sum-geometric-series}
Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$. Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
Then for some $n \in \mathbb{N}$, Then for some $n \in \mathbb{N}$,
\begin{equation} \begin{equation}
\label{sub:sum-geometric-series-eq1} \hyperlabel{sub:sum-geometric-series-eq1}
\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}. \sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.
\end{equation} \end{equation}
@ -90,7 +90,7 @@ Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$. Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
By definition, for all $k \in \mathbb{N}$, By definition, for all $k \in \mathbb{N}$,
\begin{equation} \begin{equation}
\label{sub:sum-geometric-series-eq2} \hyperlabel{sub:sum-geometric-series-eq2}
a_k = a_0r^k. a_k = a_0r^k.
\end{equation} \end{equation}
Define predicate $P(n)$ as "identity \eqref{sub:sum-geometric-series-eq1} Define predicate $P(n)$ as "identity \eqref{sub:sum-geometric-series-eq1}

3
preamble.tex
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@ -38,6 +38,9 @@
\hypersetup{colorlinks=true, linkcolor=blue, urlcolor=blue} \hypersetup{colorlinks=true, linkcolor=blue, urlcolor=blue}
\newcommand{\textref}[1]{\text{\nameref{#1}}} \newcommand{\textref}[1]{\text{\nameref{#1}}}
\newcommand{\hyperlabel}[1]{%
\label{#1}%
\hypertarget{#1}{}}
\newcommand\@leanlink[4]{% \newcommand\@leanlink[4]{%
\textcolor{blue}{$\pmb{\exists}\;{-}\;$}\href{#1/#2.html\##3}{#4}} \textcolor{blue}{$\pmb{\exists}\;{-}\;$}\href{#1/#2.html\##3}{#4}}