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set_theory

Basic idea

Foundation of modern math: everything is built from sets and membership ($\in$). Relations and functions are themselves sets of ordered pairs.

Key formulas

  • Membership: $x \in A$

  • Subset: $A \subseteq B \iff \forall x., x\in A \Rightarrow x\in B$

  • Union/intersection/difference: $A\cup B$, $A\cap B$, $A\setminus B$

  • Cartesian product: $A\times B = {(a,b) : a\in A, b\in B}$

  • Relation $R$ on $X$: $R \subseteq X\times X$

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