Relation

A relation on a set $A$ is a subset $R\subseteq A\times A$. The statement $(x,y)\in R$ is often abbreviated as $xRy$, and $(x,y)\notin R$ is abbreviated as $x/Ry$.

Context

Relations generalize the idea of “how two elements are connected.” For example, “less than” on integers is a relation: $R=\{(a,b):a<b\}$. Relations can have properties like reflexivity, symmetry, and transitivity, leading to special types like equivalence relations.

See Also

• equivalence relation
• set
• ordered pair
• cartesian product
• function