pairwise disjoint en · ADJ
Meanings
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(not-comparable, of a collection of two or more sets) Let A_λ_(λ∈Λ) be any collection of sets indexed by a set Λ. We call the indexed collection pairwise disjoint if for any two distinct indices, λ,μ∈Λ, the sets A_λ and A_μ 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,…1/2ⁿ,…,etc., then we would certainly like to be able to say that the measure of their union we is the sum ∑1/2ⁿ=1 which would not follow from finite additivity.
Proposition 4.5. Every permutation is a product of pairwise disjoint cycles, and this decomposition is unique up to the order of the terms.
2007, Pierre Antoine Grillet, Abstract Algebra, 2nd edition, Springer, page 61:To show that all #92;Gamma#95;i-translates of F#95;i, are pairwise disjoint, it suffices to show that all #92;Gamma#95;#123;i,0#125;-translates of F#95;i are pairwise disjoint, since then the argument as above will show inductively that the #92;Gamma#95;#123;i,m#125;-translates of F#95;i are pairwise disjoint for all mgt;0.
2015, Su Gao, Stephen C Jackson, Brandon Seward, Group Colorings and Bernoulli Subflows, American Mathematical Society, page 158:
Synonyms
mutually disjoint (such that any two distinct sets are disjoint)
Translations (13)
fr disjoints deux à deux (such that any two distinct sets are disjoint) · nl paarsgewijs disjunct (such that any two distinct sets are disjoint) · nl wederzijds disjunct (such that any two distinct sets are disjoint) · fr mutuellement disjoints (such that any two distinct sets are disjoint) · es disjuntos por pares (such that any two distinct sets are disjoint) · cmn 兩兩不交 /两两不交 (such that any two distinct sets are disjoint) · it a due a due disgiunti (such that any two distinct sets are disjoint) · ca disjunts dos a dos (such that any two distinct sets are disjoint) · ca mútuament disjunts (such that any two distinct sets are disjoint) · es mutuamente disjuntos (such that any two distinct sets are disjoint) · it insiemi mutuamente disgiunti (such that any two distinct sets are disjoint) · de paarweise disjunkt (such that any two distinct sets are disjoint) · id saling terlepas (such that any two distinct sets are disjoint)