pairwise disjoint
Adjective
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Adjective
pairwise disjoint (not comparable)
- (mathematics, set theory, of a collection of two or more sets) Such that any two distinct sets are disjoint (have an intersection equal to the empty set).
- 2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2nd Edition, page 61 ↗,
- Proposition 4.5. Every permutation is a product of pairwise disjoint cycles, and this decomposition is unique up to the order of the terms.
- 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,\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 \sum 1/2^n=1 which would not follow from finite additivity.
- 2015, Su Gao, Stephen C Jackson, Brandon Seward, Group Colorings and Bernoulli Subflows, American Mathematical Society, page 158 ↗,
- To show that all \Gamma_i-translates of F_i, are pairwise disjoint, it suffices to show that all \Gamma_{i,0}-translates of F_i are pairwise disjoint, since then the argument as above will show inductively that the \Gamma_{i,m}-translates of F_i are pairwise disjoint for all m>0.
- 2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2nd Edition, page 61 ↗,
- (such that any two distinct sets are disjoint) mutually disjoint
- Italian: insiemi mutuamente disgiunti, a due a due disgiunti
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.005