Meanings
- not comparablemathematicsLet 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.
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 612 more examples
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.
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 158Synonyms: mutually disjoint
Synonyms & antonyms
adjectiveLet 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.
Translations
Catalan mútuament disjunts, disjunts dos a dos
- mútuament disjuntssuch that any two distinct sets are disjoint
- disjunts dos a dossuch that any two distinct sets are disjoint
Chinese Mandarin 兩兩不交 /两两不交
- 兩兩不交 /两两不交 (liǎng liǎng bù jiāo)such that any two distinct sets are disjoint
Dutch paarsgewijs disjunct, wederzijds disjunct
- paarsgewijs disjunctsuch that any two distinct sets are disjoint
- wederzijds disjunctsuch that any two distinct sets are disjoint
French disjoints deux à deux, mutuellement disjoints
- disjoints deux à deuxsuch that any two distinct sets are disjoint
- mutuellement disjointssuch that any two distinct sets are disjoint
German paarweise disjunkt
- paarweise disjunktsuch that any two distinct sets are disjoint
Indonesian saling terlepas
- saling terlepassuch that any two distinct sets are disjoint
Italian insiemi mutuamente disgiunti, a due a due disgiunti
- insiemi mutuamente disgiuntisuch that any two distinct sets are disjoint
- a due a due disgiuntisuch that any two distinct sets are disjoint
Spanish disjuntos por pares, mutuamente disjuntos
- disjuntos por paressuch that any two distinct sets are disjoint
- mutuamente disjuntossuch that any two distinct sets are disjoint
Cite this entry
pairwise disjoint. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/pairwise%20disjoint
“pairwise disjoint.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/pairwise%20disjoint. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “pairwise disjoint,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/pairwise%20disjoint.
Source: pairwise disjoint on Wiktionary, CC BY-SA 4.0.