Added set size draft

Advanced/Size of Sets/main.tex

@@ -0,0 +1,61 @@
+% use [nosolutions] flag to hide solutions.
+% use [solutions] flag to show solutions.
+\documentclass[
+	solutions,
+	singlenumbering
+]{../../resources/ormc_handout}
+
+\uptitlel{Advanced 1}
+\uptitler{Summer 2023}
+\title{The Size of Sets, Part 1}
+\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 dense.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}
+
+	\vfill
+
+
+	\problem{}
+	Let $R$ be the set of all sets that do not contain themselves. \par
+	Does $R$ exist? \par
+	\hint{If $R$ exists, do we get a contradiction?}
+	\vfill
+
+
+	\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}