title: "Relation"

Relation

Definition. A relation on a set $A$ is a set of ordered pairs $R \subseteq A \times A$ (see Cartesian Product); we write $a \mathrel{R} b$ to mean $(a, b) \in R$. The recurring properties are reflexive ($a \mathrel{R} a$ for all $a$), symmetric ($a \mathrel{R} b$ implies $b \mathrel{R} a$), and transitive ($a \mathrel{R} b$ and $b \mathrel{R} c$ imply $a \mathrel{R} c$).

A relation with all three properties is an Equivalence Relation. Defined in Lecture 2.