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