Definition:Endorelation/Also known as

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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.

Hence 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 1974: P.M. Cohn: Algebra: Volume $\text { 1 }$, 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.


Sources