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MA1511/sets.tex

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+\input{decls.tex}
+\title{Sets}
+\begin{document}
+\maketitle
+Set comprehensions can be written $\{ x | x \in \N \}$ or $\{ x : x \in \N \}$ - '$:$' or '$|$'
+\begin{description}
+	\item[Axiom of Extensionality / Set Equality] $A = B \iff \forall x. (x \in A \iff x \in B)$
+	\item[$A \subseteq B$] \quad $\forall x \in A. x \in B$ \\
+		Is transitive, reflexive, antisymmetric
+	\item[$A \subset B$] \quad $(\forall x \in A.~x \in B) \land (\exists x \in B.~x \not\in A)$ \\
+		Is transitive, antisymmetric
+	\item[$\varnothing$] $\{\}$
+	\item[$\cup$] Union
+	\item[$\cap$] Intersection
+	\item[$A \setminus B$] \quad $\{ x \in A : x \not\in B \}$
+\end{description}
+\end{document}