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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. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...
In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ...
In mathematics, an element (also called a member) is an object contained in a set (or more generally a class). ...
Formally, two sets A and B are disjoint if their intersection is the empty set, i.e. if In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. ...
In mathematics, the empty set is the set with no elements. ...
This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if any two distinct sets in the collection are disjoint.
Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j, In mathematics, an index set is another name for a function domain. ...
For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection, then clearly its intersection is empty: However, the converse is not true: the intersection of the collection {{1, 2, 3}, {4, 5, 6}, {3, 4}} is empty, but the collection is not pairwise disjoint.
A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint and A partition of U into 6 blocks: a Venn diagram representation. ...
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