Definition:One-to-One Relation

Definition

A relation $\RR \subseteq S \times T$ is one-to-one if it is both many-to-one and one-to-many.

That is, every element of the domain of $\RR$ relates to no more than one element of its codomain, and every element of the image is related to by exactly one element of its domain.

Examples

Monogamous Society

One-to-One Relation/Examples/Monogamous Society

Also see

Compare this with a one-to-one mapping, in which every element of the domain is mapped to an element of the codomain.

• Results about one-to-one relations can be found here.

Sources

• 1939: E.G. Phillips: A Course of Analysis (2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Number: $1.2$ Fundamental notions