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