Editing Enumeration (section)

{{Short description|Ordered listing of items in collection}}
{{About||enumeration types in programming languages|Enumerated type|enumeration algorithms|Enumeration algorithm|the process of determining the number of elements in a set|Counting}}

An '''enumeration''' is a complete, ordered [[list]]ing of all the items in a collection. The term is commonly used in [[mathematics]] and [[computer science]] to refer to a listing of all of the [[element (mathematics)|element]]s of a [[Set (mathematics)|set]]. The precise requirements for an enumeration (for example, whether the set must be [[finite set|finite]], or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem.

Some sets can be enumerated by means of a '''natural ordering''' (such as 1, 2, 3, 4, ... for the set of [[positive integer]]s), but in other cases it may be necessary to impose a (perhaps arbitrary) ordering. In some contexts, such as [[enumerative combinatorics]], the term ''enumeration'' is used more in the sense of ''[[counting]]'' – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements.