In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint. Generalizations This definition of disjoint sets can be extended to a family of sets : the family is pairwise disjoint, or mutually disjoint if whenever . Alternatively, some authors use the term disjoint to refer to this notion as well. For families the notion of pairwise disjoint or mutually disjoint is sometimes defined in a subtly different manner, in that repeated identical members are allowed: the family is pairwise disjoint if whenever (every two distinct sets in the family are disjoint). For example, the collection of sets is disjoint, as is the set of the two parity classes of integers; the family with 10 members is not disjoint (because the classes of even and odd numbers are each present five times), but it is pairwise disjoint according to this definition (since one only gets a non-empty intersection of two members when the two are the same class). Two sets are said to be almost disjoint sets if their intersection is small in some sense. For instance, two infinite sets whose intersection is a finite set may be said to be almost disjoint. In topology, there are various notions of separated sets with more strict conditions than disjointness. For instance, two sets may be considered to be separated when they have disjoint closures or disjoint neighborhoods. Similarly, in a metric space, positively separated sets are sets separated by a nonzero distance. Intersections Disjointness of two sets, or of a family of sets, may be expressed in terms of intersections of pairs of them. Two sets A and B are disjoint if and only if their intersection is the empty set. It follows from this definition that every set is disjoint from the empty set, and that the empty set is the only set that is disjoint from itself. If a collection contains at least two sets, the condition that the collection is disjoint implies that the intersection of the whole collection is empty. However, a collection of sets may