# 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, 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 $T$**.