# Definition:One-to-One Relation

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## 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