Enumeration

In mathematics and theoretical computer science, an enumeration of a set is a procedure for listing all members of the set in some definite sequence. Formally, an enumeration of a set S is a mapping from (the natural numbers) to S which is surjective (i.e., every element of S is the image of at least one natural number).

It varies between authors and subdisciplines whether this mapping is also required to be injective (i.e., every element of S is the image of exactly one natural number), and/or allowed to be partial (i.e., the mapping is defined only for some natural numbers). In many applications, these differences are of little importance, because one is often concerned only with the mere existence of some enumeration, and an enumeration according to a liberal definition will generally imply that enumerations satisfying stricter requirements also exist.