## ::Enumeration

### ::concepts

''S''::natural Finite::theory Number::function Elements::mathbb Element::listing Defined::ordinal

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An **enumeration** is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and theoretical computer science (as well as applied 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 one is working in.

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.

**Enumeration sections**

Intro Enumeration in combinatorics Enumeration in set theory Enumeration in computability theory See also References External links

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