equivalence relation

This term is a technical cornerstone of set theory and abstract algebra. It describes a specific type of relationship that allows elements of a set to be grouped together based on a shared property, effectively treating different elements as identical within a certain context. The three required properties—reflexivity, symmetry, and transitivity—must all be satisfied for the relation to qualify.

In mathematical discourse, this is distinct from a general relation or a function. It is most frequently used when defining quotient sets or partitions, where the focus shifts from individual elements to the equivalence classes they inhabit.