Definition:Endorelation/Also known as

Endorelation: Also known as
The term endorelation is rarely seen. Once it is established that the domain and codomain of a given relation are the same, further comment is rarely needed.

An endorelation on $S$ is also called a relation in $S$, or a relation on $S$. The latter term is discouraged, though, because it can also mean a left-total relation, and confusion can arise.

Some sources use the term binary relation exclusively to refer to a binary endorelation.

Some sources, for example, use the term relation for what is defined here as an endorelation, and a relation defined as a general ordered triple of sets: $\tuple {S, T, R \subseteq S \times T}$ is called a correspondence.

As this can cause confusion with the usage of correspondence to mean a relation which is both left-total and right-total, it is recommended that this is not used.