Phrase guide

pairwise disjoint

adj · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

adj

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: mathematics, sciences, set-theory

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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

13 source translations are retained for this English entry.

  • Catalan: mútuament disjunts — such that any two distinct sets are disjoint
  • Catalan: disjunts dos a dos — such that any two distinct sets are disjoint
  • Chinese Mandarin: 兩兩不交 /两两不交 (liǎng liǎng bù jiāo) — such that any two distinct sets are disjoint
  • Dutch: paarsgewijs disjunct — such that any two distinct sets are disjoint
  • Dutch: wederzijds disjunct — such that any two distinct sets are disjoint
  • French: disjoints deux à deux — such that any two distinct sets are disjoint
  • French: mutuellement disjoints — such that any two distinct sets are disjoint
  • German: paarweise disjunkt — such that any two distinct sets are disjoint
  • Indonesian: saling terlepas — such that any two distinct sets are disjoint
  • Italian: insiemi mutuamente disgiunti — such that any two distinct sets are disjoint
  • Italian: a due a due disgiunti — such that any two distinct sets are disjoint
  • Spanish: disjuntos por pares — such that any two distinct sets are disjoint
  • Spanish: mutuamente disjuntos — such that any two distinct sets are disjoint