What does pairwise disjoint mean?

pairwise disjoint

Word Rarity Very rare

Frequency: Zipf frequency 2.16 in modern English

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adj

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.

"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,…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."

mutually disjoint