See pairwise disjoint on Wiktionary
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"examples": [
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"ref": "2007, Pierre Antoine Grillet, Abstract Algebra, 2nd edition, Springer, page 61:",
"text": "Proposition 4.5. Every permutation is a product of pairwise disjoint cycles, and this decomposition is unique up to the order of the terms.",
"type": "quote"
},
{
"text": "2009, John M. Franks, A (Terse) Introduction to Lebesgue Integration, American Mathematical Society, page 27,\nFor 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."
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"ref": "2015, Su Gao, Stephen C Jackson, Brandon Seward, Group Colorings and Bernoulli Subflows, American Mathematical Society, page 158:",
"text": "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.",
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"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."
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"(mathematics, set theory, of a collection of two or more sets) 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."
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"sense": "such that any two distinct sets are disjoint",
"word": "mutually disjoint"
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"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "such that any two distinct sets are disjoint",
"word": "mútuament disjunts"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "such that any two distinct sets are disjoint",
"word": "disjunts dos a dos"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "such that any two distinct sets are disjoint",
"word": "paarsgewijs disjunct"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "such that any two distinct sets are disjoint",
"word": "wederzijds disjunct"
},
{
"code": "fr",
"lang": "French",
"sense": "such that any two distinct sets are disjoint",
"word": "disjoints deux à deux"
},
{
"code": "fr",
"lang": "French",
"sense": "such that any two distinct sets are disjoint",
"word": "mutuellement disjoints"
},
{
"code": "de",
"lang": "German",
"sense": "such that any two distinct sets are disjoint",
"word": "paarweise disjunkt"
},
{
"code": "id",
"lang": "Indonesian",
"sense": "such that any two distinct sets are disjoint",
"word": "saling terlepas"
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"code": "it",
"lang": "Italian",
"sense": "such that any two distinct sets are disjoint",
"tags": [
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"word": "insiemi mutuamente disgiunti"
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"code": "cmn",
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"roman": "liǎng liǎng bù jiāo",
"sense": "such that any two distinct sets are disjoint",
"word": "兩兩不交 /两两不交"
},
{
"code": "es",
"lang": "Spanish",
"sense": "such that any two distinct sets are disjoint",
"word": "disjuntos por pares"
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{
"code": "es",
"lang": "Spanish",
"sense": "such that any two distinct sets are disjoint",
"word": "mutuamente disjuntos"
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"word": "pairwise disjoint"
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"text": "2009, John M. Franks, A (Terse) Introduction to Lebesgue Integration, American Mathematical Society, page 27,\nFor 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."
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"code": "ca",
"lang": "Catalan",
"sense": "such that any two distinct sets are disjoint",
"word": "mútuament disjunts"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "such that any two distinct sets are disjoint",
"word": "disjunts dos a dos"
},
{
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"lang": "Dutch",
"sense": "such that any two distinct sets are disjoint",
"word": "paarsgewijs disjunct"
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"lang": "Dutch",
"sense": "such that any two distinct sets are disjoint",
"word": "wederzijds disjunct"
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{
"code": "fr",
"lang": "French",
"sense": "such that any two distinct sets are disjoint",
"word": "disjoints deux à deux"
},
{
"code": "fr",
"lang": "French",
"sense": "such that any two distinct sets are disjoint",
"word": "mutuellement disjoints"
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{
"code": "de",
"lang": "German",
"sense": "such that any two distinct sets are disjoint",
"word": "paarweise disjunkt"
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"code": "id",
"lang": "Indonesian",
"sense": "such that any two distinct sets are disjoint",
"word": "saling terlepas"
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"sense": "such that any two distinct sets are disjoint",
"tags": [
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"word": "insiemi mutuamente disgiunti"
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"code": "it",
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"sense": "such that any two distinct sets are disjoint",
"tags": [
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"word": "a due a due disgiunti"
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"code": "cmn",
"lang": "Mandarin",
"roman": "liǎng liǎng bù jiāo",
"sense": "such that any two distinct sets are disjoint",
"word": "兩兩不交 /两两不交"
},
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"code": "es",
"lang": "Spanish",
"sense": "such that any two distinct sets are disjoint",
"word": "disjuntos por pares"
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{
"code": "es",
"lang": "Spanish",
"sense": "such that any two distinct sets are disjoint",
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"word": "pairwise disjoint"
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