A set X is an unordered collection of objects, which are called the elements of *X*. For example, the three languages French, Russian and Chinese form a set, which we denote as *X* = {French, Russian, Chinese} (or equivalently, {Chinese, French, Russian} as order does not matter).

#### Subset (or cluster)

A set *Y* is a *subset* of a set *X* if every element in *Y* is also contained in *X*. For example, {French, Russian} is a subset of the set {French, Russian, Chinese}. Sometimes a subset of a set which contains at least one element is also known as a *cluster*.

#### Set union

The *union of two sets* *X* and *Y*, denoted *X* U *Y* is the set formed by taking all of the elements in *X* and all elements in *Y*. For example, {French, German} U {Italian, Russian, English} = {French, German, Italian, Russian, English}

#### Set intersection

The *intersection of two sets* *X* and *Y*, denoted *X* ∩ *Y*, is the set formed by taking all those elements that are in both *X* *and* *Y*. For example, {French, German} ∩ {Italian, Russian, French} = {French}.

#### Empty set

The *empty set* is the set that contains no elements, which is usually denoted Ø.

#### Disjoint sets

Two sets are called *disjoint* if their intersection is the empty set, that is, they have no elements in common. So, for example, the two sets {French, German} and {Italian, Russian, English} are disjoint sets as their intersection is the empty set, i.e. {French, German} ∩ {Italian, Russian, English} = Ø.

#### Complement of a set

If *Y* is a subset of a set *X* then the *complement* of *Y* in *X*, denoted by *X-Y*, comprises of all those elements in *X* that are not in *Y*. For example, the complement of {French, Chinese} in the set {French, Chinese, Russian, Italian} is {Russian, Italian}.

See also the entry split. The Wikipedia page set (mathematics) provides a very informative introduction to sets.

**In other languages**

DE: Menge, Untermenge, Vereinigungsmenge, Schnittmenge, leere Menge, disjunkte Mengen, komplementäre Mengen

FR: ensemble, sous-ensemble, union d'ensembles, intersection d'ensembles, ensembles disjoints, ensembles complémentaires

IT: insieme, sottoinsieme, unione d'insiemi, intersezione d'insiemi, insieme vuoto, insiemi disgiunti, insieme complementare / complemento (di un insieme)