containselement

Containselement is a predicate used in mathematics and computer science to express whether a container includes a given element. In set theory, the statement “A contains element x” is true precisely when x is a member of A, commonly written as x ∈ A. Equivalently, containselement(A, x) holds if and only if x ∈ A.

In the context of multisets, the predicate may take multiplicity into account: containselement(A, x) is true if the number of occurrences of x in A is greater than zero. For ordinary sets, multiplicity is not a factor, and containselement reduces to membership.

In programming languages, containers often provide a contains or has method to test membership. For example, A.contains(x) or x in A returns a boolean indicating whether x is an element of the container. The exact semantics can vary with data structure (lists, arrays, sets, maps) and with language features such as handling of null values or duplicates.

Containselement is related but distinct from the subset relation. If B is a set, A ⊇ B expresses that A contains every element of B, whereas containselement(A, x) concerns only a single element x and whether it belongs to A.

Applications include formal specifications, query languages, data validation, and automated reasoning, where explicit membership tests help define properties of containers, sequences, and collections.

See also: membership, element of, contains operator, subset, multiset.