A list of items in order. Thus the items are organized in such a way that they can be counted, and for each nonnegative integer i within an appropriate range there is a unique item associated with it. An enumeration may be finite or infinite; when an infinite set is involved, the infinite set must be countable. An enumeration is said to be effective if there is an algorithm for producing the enumeration.
Enumeration is used to define data types in languages of the Pascal and Jovial families. It also plays a significant role in combinatorics where one might typically talk of an enumeration of permutations or combinations, of binary trees, of graphs, of groups, etc.