Routledge Dictionary of Language and Linguistics.pdf

A-Z 437FulaniFulafunction (also mapping)1 Basic term in set theory taken from geometry: assignment to each element x of a set A(= domain) exactly one element y=f(x) of a set B (=range) (notation: f: A→B or A→B).In set theory, f frepresents a subset of the product set A ×B, namely the subset of theordered pairs ‹x, y› with xεA and y=f(x) εB. Types of functions are as follows: (a)Injection: a function f of A into B is injective (or unidirectional), if f is left-directional,that is if the equation f(x) =f(y) consistently yields x=y.(b) Surjection (=mapping onto): a function f of A into B is surjective if every element in Bis the value of at least one element x in A under ƒ.(c) Bijection: a function is bijective or unidirectional up if it is both injective andsurjective.