# 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 $T$**.

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):**correspondence** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**correspondence**