Definition:Many-to-One Relation

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

$$\mathcal{R}\subseteq S \times T: \forall x \in \mathrm{Dom} \left({\mathcal{R}}\right): \left({x, y_1}\right) \in \mathcal{R}\land \left({x, y_2}\right) \in \mathcal{R} \Longrightarrow y_1 = y_2$$

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

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