pairwise disjoint
adj1
Mathematics, Sciences, Set theory 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.
Of a collection of two or more sets
- 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:
- 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.
1 more example
- 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