nelements

Nelements is a term used to describe the number of elements in a set, sequence, or other finite collection. In mathematics, it is common to denote this size by n, and to write the cardinality of a set A as |A| = n. The expression n-elements or an n-element set is used to emphasize the exact size of the collection.

For finite sets, there exists a nonnegative integer n such that |A| = n. The case n = 0 corresponds to the empty set. If a set is infinite, its size is described by an infinite cardinal rather than a finite n; discussions of nelements are then supplemented by the concept of cardinality.

In counting and combinatorics, the value of n determines many standard results. For example, the number of permutations of n distinct elements is n!, and the number of k-element subsets of an n-element set is the binomial coefficient C(n, k). In probability and statistics, sample spaces with n equally likely outcomes are common.

In computer science and data processing, nelements often refers to the length or size of a data structure, such as an array or list. Functions or methods that report nelements allow loops, indexing, and capacity planning. Practically, the word appears in documentation and algorithms to distinguish size from content.

See also: cardinality, finite set, infinity, permutation, combination, array length.