A function is a relation (a set of ordered pairs) with the additional property that: no two pairs have the same first element and different second elements.
The definition is often stated as: A relation in which every x value is associated with exactly one y value. "Exactly one means one but two or more:
{(1,2);(2,3);(3,4);(2,5)} includes the points (2,3) and (2,5). Therefore these set of pairs are not a function.
