See pairwise disjoint on Wiktionary
Download JSON data for pairwise disjoint meaning in All languages combined (4.6kB)
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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": "quotation"
},
{
"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."
},
{
"ref": "2015, Su Gao, Stephen C Jackson, Brandon Seward, Group Colorings and Bernoulli Subflows, American Mathematical Society, page 158",
"text": "To show that all #x5C;Gamma#x5F;i-translates of F#x5F;i, are pairwise disjoint, it suffices to show that all #x5C;Gamma#x5F;#x7B;i,0#x7D;-translates of F#x5F;i are pairwise disjoint, since then the argument as above will show inductively that the #x5C;Gamma#x5F;#x7B;i,m#x7D;-translates of F#x5F;i are pairwise disjoint for all m#x3E;0.",
"type": "quotation"
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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."
],
"id": "en-pairwise_disjoint-en-adj-z7Ed-H5~",
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"raw_glosses": [
"(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."
],
"raw_tags": [
"of a collection of two or more sets"
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"synonyms": [
{
"sense": "such that any two distinct sets are disjoint",
"word": "mutually disjoint"
}
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"tags": [
"not-comparable"
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"topics": [
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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"
},
{
"code": "it",
"lang": "Italian",
"sense": "such that any two distinct sets are disjoint",
"tags": [
"masculine"
],
"word": "insiemi mutuamente disgiunti"
},
{
"code": "it",
"lang": "Italian",
"sense": "such that any two distinct sets are disjoint",
"tags": [
"masculine"
],
"word": "a due a due disgiunti"
},
{
"code": "cmn",
"lang": "Mandarin",
"sense": "such that any two distinct sets are disjoint",
"word": "兩兩不交"
},
{
"code": "cmn",
"lang": "Mandarin",
"roman": "liǎng liǎng bù jiāo",
"sense": "such that any two distinct sets are disjoint",
"word": "两两不交"
},
{
"code": "es",
"lang": "Spanish",
"sense": "such that any two distinct sets are disjoint",
"word": "disjuntos por pares"
},
{
"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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"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": "quotation"
},
{
"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."
},
{
"ref": "2015, Su Gao, Stephen C Jackson, Brandon Seward, Group Colorings and Bernoulli Subflows, American Mathematical Society, page 158",
"text": "To show that all #x5C;Gamma#x5F;i-translates of F#x5F;i, are pairwise disjoint, it suffices to show that all #x5C;Gamma#x5F;#x7B;i,0#x7D;-translates of F#x5F;i are pairwise disjoint, since then the argument as above will show inductively that the #x5C;Gamma#x5F;#x7B;i,m#x7D;-translates of F#x5F;i are pairwise disjoint for all m#x3E;0.",
"type": "quotation"
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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."
],
"raw_tags": [
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"synonyms": [
{
"sense": "such that any two distinct sets are disjoint",
"word": "mutually disjoint"
}
],
"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"
},
{
"code": "it",
"lang": "Italian",
"sense": "such that any two distinct sets are disjoint",
"tags": [
"masculine"
],
"word": "insiemi mutuamente disgiunti"
},
{
"code": "it",
"lang": "Italian",
"sense": "such that any two distinct sets are disjoint",
"tags": [
"masculine"
],
"word": "a due a due disgiunti"
},
{
"code": "cmn",
"lang": "Mandarin",
"sense": "such that any two distinct sets are disjoint",
"word": "兩兩不交"
},
{
"code": "cmn",
"lang": "Mandarin",
"roman": "liǎng liǎng bù jiāo",
"sense": "such that any two distinct sets are disjoint",
"word": "两两不交"
},
{
"code": "es",
"lang": "Spanish",
"sense": "such that any two distinct sets are disjoint",
"word": "disjuntos por pares"
},
{
"code": "es",
"lang": "Spanish",
"sense": "such that any two distinct sets are disjoint",
"word": "mutuamente disjuntos"
}
],
"word": "pairwise disjoint"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-12 from the enwiktionary dump dated 2024-05-02 using wiktextract (ae36afe and 304864d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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