threeset

Threeset is a term occasionally used to describe a set consisting of exactly three elements. In standard mathematical terminology, a three-element set is usually called a 3-element set or simply a set with cardinality three; the phrase “threeset” appears mainly as informal shorthand or in specific texts and software documentation. A threeset contains three distinct elements, since a set contains no repeated elements by definition.

A threeset can be represented by any unordered collection of three elements, typically written as {a, b, c}. When the order of elements matters, the corresponding object is usually referred to as a 3-tuple or ordered triple, not a threeset. The distinction between a set and a sequence is important in combinatorics and related fields.

Counting threesets from a finite universe: if the universe contains n elements, the number of distinct threesets that can be formed is the binomial coefficient C(n, 3) = n(n−1)(n−2)/6. If order matters, the number of ordered threesets (often called 3-permutations) is n(n−1)(n−2).

Relation to other concepts: a threeset is a special case of a subset and is related to the idea of a triple or 3-element combination. In contrast, a triplet or 3-tuple denotes an ordered collection of three elements. In some programming or database contexts, the term threeset might be used informally to name variables or data structures that store three values.

Notes: “threeset” is not a standard formal term in most mathematical references; when precision is required, it is preferable to say “three-element set” or “set with cardinality three.” See also set, triple, 3-element set, and combination.