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Further normalize links to Lean from TeX.

finite-set-exercises
Joshua Potter 2023-05-06 12:34:05 -06:00
parent 74f52f02b8
commit d4dd6b1ba7
6 changed files with 72 additions and 52 deletions
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37
Bookshelf/Real/Sequence.tex
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@ -1,37 +0,0 @@
\documentclass{article}
\input{preamble}
\newcommand{\ns}{Real}
\newcommand{\linkA}[1]{\href{../Sequence/Arithmetic.html\#\ns.#1}{\ns.#1}}
\newcommand{\linkG}[1]{\href{../Sequence/Geometric.html\#\ns.#1}{\ns.#1}}
\begin{document}
\section*{Sum of Arithmetic Series}%
\label{sec:sum-arithmetic-series}
Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$
\begin{proof}
\linkA{Arithmetic.sum\_recursive\_closed}
\end{proof}
\section*{Sum of Geometric Series}%
\label{sec:sum-geometric-series}
Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$
\begin{proof}
\linkG{Geometric.sum\_recursive\_closed}
\end{proof}
\end{document}

23
Bookshelf/Real/Sequence/Arithmetic.tex Normal file
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@ -0,0 +1,23 @@
\documentclass{article}
\input{preamble}
\newcommand{\link}[1]{\lean{../../..}{Bookshelf/Real/Sequence/Arithmetic}
{Real.Arithmetic.#1}}
\begin{document}
\section*{Sum of Arithmetic Series}%
\label{sec:sum-arithmetic-series}
Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$
\begin{proof}
\link{sum_recursive_closed}
\end{proof}
\end{document}

23
Bookshelf/Real/Sequence/Geometric.tex Normal file
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@ -0,0 +1,23 @@
\documentclass{article}
\input{preamble}
\newcommand{\link}[1]{\lean{../../..}{Bookshelf/Real/Sequence/Geometric}
{Real.Geometric.#1}}
\begin{document}
\section*{Sum of Geometric Series}%
\label{sec:sum-geometric-series}
Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
Then for some $n \in \mathbb{N}$,
$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$
\begin{proof}
\link{sum_recursive_closed}
\end{proof}
\end{document}

22
Exercises/Apostol/Chapter_I_3.tex
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@ -3,8 +3,8 @@
\input{preamble} \input{preamble}
\newcommand{\ns}{Exercises.Apostol.Chapter\_I\_3.Real} \newcommand{\link}[1]{\lean{../..}{Exercises/Apostol/Chapter_I_3}
\newcommand{\link}[1]{\href{../Chapter_I_3.html\#\ns.#1}{\ns.#1}} {Exercises.Apostol.Chapter\_I\_3.Real.#1}}
\begin{document} \begin{document}
@ -16,7 +16,7 @@ is, there is a real number $L$ such that $L = \inf{S}$.
\begin{proof} \begin{proof}
\link{exists\_isGLB} \link{exists_isGLB}
\end{proof} \end{proof}
@ -27,7 +27,7 @@ For every real $x$ there exists a positive integer $n$ such that $n > x$.
\begin{proof} \begin{proof}
\link{exists\_pnat\_geq\_self} \link{exists_pnat_geq_self}
\end{proof} \end{proof}
@ -39,7 +39,7 @@ integer $n$ such that $nx > y$.
\begin{proof} \begin{proof}
\link{exists\_pnat\_mul\_self\_geq\_of\_pos} \link{exists_pnat_mul_self_geq_of_pos}
\end{proof} \end{proof}
@ -52,7 +52,7 @@ for every integer $n \geq 1$, then $x = a$.
\begin{proof} \begin{proof}
\link{forall\_pnat\_leq\_self\_leq\_frac\_imp\_eq} \link{forall_pnat_leq_self_leq_frac_imp_eq}
\end{proof} \end{proof}
@ -70,8 +70,8 @@ Let $h$ be a given positive number and let $S$ be a set of real numbers.
\begin{proof} \begin{proof}
\begin{enumerate}[(a)] \begin{enumerate}[(a)]
\item \link{sup\_imp\_exists\_gt\_sup\_sub\_delta} \item \link{sup_imp_exists_gt_sup_sub_delta}
\item \link{inf\_imp\_exists\_lt\_inf\_add\_delta} \item \link{inf_imp_exists_lt_inf_add_delta}
\end{enumerate} \end{enumerate}
\end{proof} \end{proof}
@ -92,8 +92,8 @@ $$C = \{a + b : a \in A, b \in B\}.$$
\begin{proof} \begin{proof}
\begin{enumerate}[(a)] \begin{enumerate}[(a)]
\item \link{sup\_minkowski\_sum\_eq\_sup\_add\_sup} \item \link{sup_minkowski_sum_eq_sup_add_sup}
\item \link{inf\_minkowski\_sum\_eq\_inf\_add\_inf} \item \link{inf_minkowski_sum_eq_inf_add_inf}
\end{enumerate} \end{enumerate}
\end{proof} \end{proof}
@ -109,7 +109,7 @@ $$\sup{S} \leq \inf{T}.$$
\begin{proof} \begin{proof}
\link{forall\_mem\_le\_forall\_mem\_imp\_sup\_le\_inf} \link{forall_mem_le_forall_mem_imp_sup_le_inf}
\end{proof} \end{proof}

6
Exercises/Enderton/Chapter0.tex
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@ -2,8 +2,8 @@
\input{preamble} \input{preamble}
\newcommand{\ns}{Exercises.Enderton.Chapter0} \newcommand{\link}[1]{\lean{../..}{Exercises/Enderton/Chapter0}
\newcommand{\link}[1]{\href{../Chapter0.html\#\ns.#1}{\ns.#1}} {Exercises.Enderton.Chapter0.#1}}
\begin{document} \begin{document}
@ -15,7 +15,7 @@ Then $x_1 = \langle y_1, \ldots, y_{k+1} \rangle$.
\begin{proof} \begin{proof}
\link{lemma\_0a} \link{lemma_0a}
\end{proof} \end{proof}

13
preamble.tex
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@ -1,6 +1,6 @@
\usepackage{amsfonts, amsthm} \usepackage{amsfonts, amsthm}
\usepackage[T1]{fontenc}
\usepackage{hyperref} \usepackage{hyperref}
\usepackage{underscore}
\newtheorem{theorem}{Theorem} \newtheorem{theorem}{Theorem}
\newtheorem{xtheoreminner}{Theorem} \newtheorem{xtheoreminner}{Theorem}
@ -10,3 +10,14 @@
}{\endxtheoreminner} }{\endxtheoreminner}
\hypersetup{colorlinks=true, urlcolor=blue} \hypersetup{colorlinks=true, urlcolor=blue}
% https://tex.stackexchange.com/a/232188
\newcommand{\startunderscoreletter}{\catcode`_ 12\relax}
\newcommand{\stopunderscoreletter}{\catcode`_ 8\relax}
% The first argument refers to a relative path upward from a current file to
% the root of the workspace (i.e. where this `preamble.tex` file is located).
% We include an additional nesting of `..` to account for the generated `LaTeX`
% directory automatically included when generating documentation.
\newcommand{\lean}[3]{\href{#1/../#2.html\##3}{
\startunderscoreletter #3 \stopunderscoreletter}}