# Enumeration

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 Revision as of 19:53, 5 June 2009Jahsonic (Talk | contribs)← Previous diff Current revisionJahsonic (Talk | contribs) Line 1: Line 1: {{Template}} {{Template}} - :... [[ambiguity]] is exemplified by the [[Rabelaisian]] [[list]]s and[[ enumeration]]s, which hover between [[hollow]] [[repetition]] and [[fertile]] [[creativity]]. ... ''[[Madness, masks, and laughter]]'' By [[Rupert D. V. Glasgow]] + An '''enumeration''' of a collection of items is a complete, ordered listing of all of the items in that collection. The term is commonly used in [[mathematics]] and theoretical [[computer science]] to refer to a listing of all of the [[element (mathematics)|element]]s of a [[Set (mathematics)|set]]. In statistics the term [[categorical variable]] is used rather than enumeration. 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 branch of mathematics and the context in which one is working. + + 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. + + + ==See also== + * [[Ordinal number]] + * [[Enumerative definition]] + {{GFDL}} {{GFDL}}

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An enumeration of a collection of items is a complete, ordered listing of all of the items in that collection. The term is commonly used in mathematics and theoretical computer science to refer to a listing of all of the elements of a set. In statistics the term categorical variable is used rather than enumeration. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the branch of mathematics and the context in which one is working.

Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ... for the set of positive integers), 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.