Functional relation

In mathematics and in logic, a functional relation is

(x)(x $\in$ X) & (y)(z)(y,z $\in$ Y)((Rxy & Rxz) $\to$ y = z).

The relation R is functional over X and Y.

A binary relation that is functional but not defined for every x in X is called a partial function. A binary relation that is total (i.e., defined for every x in X) and functional is called a function.