Relation/Examples/Ordering on Arbitrary Sets of Integers/Not Many-to-One

Example of Relation which is not Many-to-One
$\mathcal R$ is not a many-to-one relation.

Proof
For example we have:
 * $\tuple {1, 1} \in \mathcal R$

and:
 * $\tuple {1, 2} \in \mathcal R$

Hence $\mathcal R$ is not many-to-one by definition.