Definition:Many-to-One Relation

Definition
A relation $$\mathcal R \subseteq S \times T$$ is many-to-one if:


 * $$\mathcal R \subseteq S \times T: \forall x \in \operatorname{Dom} \left({\mathcal R}\right): \left({x, y_1}\right) \in \mathcal R \and \left({x, y_2}\right) \in \mathcal R \implies y_1 = y_2$$

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

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

Such a relation is also referred to as:
 * a functional relation;
 * a right-definite relation;
 * a right-unique relation;
 * a partial mapping.