Definition:Endorelation/General Definition
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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.
Sources
- 1993: Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (2nd ed.) ... (previous) ... (next): $\S 1$: Naive Set Theory: $\S 1.5$: Relations