Definition:Many-to-One Relation

Definition
A relation $\RR \subseteq S \times T$ is many-to-one :


 * $\forall x \in \Dom \RR: \forall y_1, y_2 \in \Cdm \RR: \tuple {x, y_1} \in \RR \land \tuple {x, y_2} \in \RR \implies y_1 = y_2$

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

Also see

 * Definition:One-to-Many Relation
 * Definition:Many-to-Many Relation

If in addition, every element of the domain relates to exactly one element in the codomain, the many-to-one relation is known as a mapping (or function).