 Disjoint sets

In mathematics, two sets are said to be disjoint if they have no element in common. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets.^{[1]}
Explanation
Formally, two sets A and B are disjoint if their intersection is the empty set, i.e. if
This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.
Formally, let I be an index set, and for each i in I, let A_{i} be a set. Then the family of sets {A_{i} : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,
For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {A_{i}} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:
However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.
A partition of a set X is any collection of nonempty subsets {A_{i} : i ∈ I} of X such that {A_{i}} are pairwise disjoint and
See also
 Almost disjoint sets
 Connectedness
 Disjoint union
 Disjointset data structure
 Independence (probability theory) (contrast)
References
 ^ "Stats: Probability Rules". People.richland.edu. http://people.richland.edu/james/lecture/m170/ch05rul.html. Retrieved 20111108.
 Weisstein, Eric W., "Disjoint Sets" from MathWorld.
Categories: Basic concepts in set theory
 Set families
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disjoint — dis•joint [[t]dɪsˈdʒɔɪnt[/t]] v. t. 1) to separate or disconnect the joints or joinings of 2) to put out of order; derange 3) to come apart 4) to be dislocated; be out of joint 5) math. Math. a) (of two sets) having no common elements b) (of a… … From formal English to slang
disjoint — 1. adjective a) not smooth or continuous; disjointed b) (not used in the comparative or superlative) Of two or more sets, having no members in common; having an intersection equal to the empty set. Ant: non disjoint … Wiktionary
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