Definition:Relation/Also known as

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