Function

is a many-to-one relation. There are, as far as I know, two styles of defining functions: Functions can be surjective (covering), injective (distinct input, distinct output), or bijective (both surjective and injective).
 * 1) Enumeration, for example, the double function on pos. natural numbers = {(1, 2), (2, 4), ...}
 * 2) Describing the rule to get the output, for example, the double function on pos. natural numbers will be like: f(x) = 2x