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Advanced handouts

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Co-authored-by: Mark <mark@betalupi.com>
Co-committed-by: Mark <mark@betalupi.com>
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Mark
2025-01-22 12:28:44 -08:00
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src/Advanced/Size of Sets/main.tex Executable file
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% use [nosolutions] flag to hide solutions.
% use [solutions] flag to show solutions.
\documentclass[
solutions,
singlenumbering
]{../../../lib/tex/ormc_handout}
\usepackage{../../../lib/tex/macros}
\uptitlel{Advanced 1}
\uptitler{\smallurl{}}
\title{The Size of Sets}
\subtitle{Prepared by Mark on \today{}}
\begin{document}
\maketitle
\input{parts/0 sets.tex}
\input{parts/1 really big.tex}
\input{parts/2 cartesian.tex}
\input{parts/3 functions.tex}
\input{parts/4 enumeration.tex}
%\input{parts/5 dense.tex}
\input{parts/6 uncountable.tex}
%\vfill
%\pagebreak
%\section{Bonus Problems}
%\problem{}
%Using only sets, how can we build an ordered pair $(a, b)$? \par
%$(a, b)$ should be equal to $(c, d)$ if and only if $a = b$ and $c = d$. \par
%Of course, $(a, b) \neq (b, a)$.
%\begin{solution}
% $(a, b) = \{ \{a\}, \{a, b\}\}$
%\end{solution}
%\problem{}
%Suppose $f: A \to B$ and $g: B \to C$ are both one-to-one. Must $h(x) = g(f(x))$ be one-to-one? \par
%Provide a proof or a counterexample.
%\vfill
%\problem{}
%Suppose $f: A \to B$ and $g: B \to C$ are both onto. Must $h(x) = g(f(x))$ be onto? \par
%Provide a proof or a counterexample.
%\vfill
%\pagebreak
\end{document}