Relations Are Multi-valued
For each xi in X, let Yi be the subset of Y whose members are related to xi by some relation R(x,y).
- Yi has ni members iff xi is related to ni members of Y.
Likewise for each yj there is a subset Xj of X whose members are all related to yj.
- Xj has mj members iff mj elements of X are related to yj.
If ni > 1 for at least one xi then this relation is a multivalued (generalization of) a function.
- Do not call it a function unless you explicitly identify it as multivalued.