Definition:Relation/Also known as
Relation: also known as
In this context, technically speaking, what has been defined as a relation can actually be referred to as a binary relation.
In the field of predicate logic, a relation can be seen referred to as a relational property.
Some sources use the term correspondence for what is defined here as relation, reserving the term relation for what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is defined as endorelation, that is, a relation on $S \times S$ for some set $S$.
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.
Some sources prefer the term relation between $S$ and $T$ as it can be argued that this provides better emphasis on the existence of the domain and codomain.
1968: Nicolas Bourbaki: Theory of Sets refers to a correspondence between $S$ and $T$.
The word relationship is often seen, particularly in the mundane (non-mathematical) context.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): relationship
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binary relation
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): correspondence
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binary relation
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): correspondence