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.
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
- 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.5$ Relations
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relation: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relation: 1.