# Definition:Endorelation/General Definition

## Definition

An $n$-ary relation $\RR$ on a cartesian space $S^n$ is an $n$-ary endorelation on $S$:

$\RR = \struct {S, S, \ldots, S, R}$

where $R \subseteq S^n$.

## 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 set, further comment is rarely needed.

An $n$-ary endorelation is also called an $n$-ary relation in $S$, or on $S$.

The on $S$ form is discouraged, though, because it can also mean a left-total relation, and confusion can arise.