pairwise disjoint

== English == === Adjective === pairwise disjoint (not comparable) (mathematics, set theory, of a collection of two or more sets) Let { A λ } λ ∈ Λ {\displaystyle \{A_{\lambda }\}_{\lambda \in \Lambda }} be any collection of sets indexed by a set Λ {\displaystyle \Lambda } . We call the indexed collection pairwise disjoint if for any two distinct indices, λ , μ ∈ Λ {\displaystyle \lambda ,\mu \in \Lambda } , the sets A λ {\displaystyle A_{\lambda }} and A μ {\displaystyle A_{\mu }} are disjoint. 2009, John M. Franks, A (Terse) Introduction to Lebesgue Integration, American Mathematical Society, page 27, For example, if we had a collection of pairwise disjoint intervals of length 1 / 2 , 1 / 4 , 1 / 8 , … 1 / 2 n , … {\displaystyle 1/2,1/4,1/8,\dots 1/2^{n},\dots } ,etc., then we would certainly like to be able to say that the measure of their union we is the sum ∑ 1 / 2 n = 1 {\displaystyle \sum 1/2^{n}=1} which would not follow from finite additivity. ==== Usage notes ==== The condition is a generalization of the concept of disjoint sets, from two to an arbitrary collection of sets. When applied to a collection, the original formulation - that the sets have an intersection equal to the empty set - becomes ambiguous and in need of clarification. ==== Synonyms ==== (such that any two distinct sets are disjoint): mutually disjoint ==== Translations ==== === Further reading === Disjoint sets on Wikipedia.Wikipedia Mutual exclusivity on Wikipedia.Wikipedia