An unordered collection of values where each value occurs at most once. A group of elements with three properties: (1) all elements belong to a universe, (2) either each element is a member of the set or it is not, and (3) the elements are unordered. Formal Definition: As an abstract data type, a set has a single query function, isIn(v, S), which tells whether an element is a member of the set or not, and two modifier functions, add(v, S) and remove(v, S). These may be defined with axiomatic semantics as follows.

1. new() returns a set
2. isIn(v, new()) = false
3. isIn(v, add(v, S)) = true
4. isIn(v, add(u, S)) = isIn(v , S) if v ≠ u
5. remove(v, new()) = new()
6. remove(v, add(v, S)) = remove(v, S)
7. remove(v, add(u, S)) = add(u, remove(v, S)) if v ≠ u