See partially ordered set on Wiktionary
Download JSON data for partially ordered set meaning in All languages combined (5.5kB)
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"word": "totally ordered set"
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"source": "Thesaurus:partially ordered set",
"word": "complete lattice"
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{
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"lang": "English",
"lang_code": "en",
"pos": "noun",
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"word": "complete partial order"
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"A set that has a given, elsewhere specified partial order."
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"(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order."
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{
"text": "1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28,\nA partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of \"≻\" and speak of the partially ordered set P.\nThe ordered fields defined earlier are easily seen to be examples of partially ordered sets."
},
{
"ref": "1994, I. V. Evstigneev, P. E. Greenwood, Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting, American Mathematical Society, page 35",
"text": "In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set T_M.",
"type": "quotation"
},
{
"ref": "2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, page 45",
"text": "The invention of a derivative of a finite partially ordered set by Nazarova and Roiter in the late 1960s or early 1970s was a seminal event in the subject of representations of finite partially ordered sets (see [Simson 92]).",
"type": "quotation"
}
],
"glosses": [
"The ordered pair comprising a set and its partial order."
],
"id": "en-partially_ordered_set-en-noun-8zd~fBuI",
"links": [
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"raw_glosses": [
"(set theory, order theory, formally) The ordered pair comprising a set and its partial order."
],
"synonyms": [
{
"_dis1": "40 60",
"sense": "ordered pair of set and partial order",
"word": "poset"
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"synonyms": [
{
"_dis1": "53 47",
"sense": "set on which a partial order is defined",
"word": "ground set"
},
{
"_dis1": "53 47",
"sense": "set on which a partial order is defined",
"word": "poset"
},
{
"_dis1": "50 50",
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"translations": [
{
"_dis1": "53 47",
"code": "ar",
"english": "Arabic Academy term",
"lang": "Arabic",
"roman": "fiʔatun murattabatun juzʔiyyan",
"sense": "set having a specified partial order",
"tags": [
"feminine"
],
"word": "فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
},
{
"_dis1": "53 47",
"code": "ar",
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"raw_tags": [
"in educational communities"
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"roman": "majmūʕatun murattabatun juzʔiyyan",
"sense": "set having a specified partial order",
"tags": [
"common",
"feminine"
],
"word": "مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
},
{
"_dis1": "53 47",
"code": "cs",
"lang": "Czech",
"sense": "set having a specified partial order",
"tags": [
"feminine"
],
"word": "uspořádaná množina"
},
{
"_dis1": "53 47",
"code": "fi",
"lang": "Finnish",
"sense": "set having a specified partial order",
"word": "osittain järjestetty joukko"
},
{
"_dis1": "53 47",
"code": "de",
"lang": "German",
"sense": "set having a specified partial order",
"tags": [
"feminine"
],
"word": "partiell geordnete Menge"
},
{
"_dis1": "53 47",
"alt": "はんじゅんじょしゅうごう",
"code": "ja",
"lang": "Japanese",
"roman": "hanjunjo-shūgō",
"sense": "set having a specified partial order",
"word": "半順序集合"
},
{
"_dis1": "53 47",
"code": "sv",
"lang": "Swedish",
"sense": "set having a specified partial order",
"tags": [
"common-gender"
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"word": "partiellt ordnad mängd"
}
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"wikipedia": [
"partially ordered set"
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"word": "partially ordered set"
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"word": "totally ordered set"
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{
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"word": "complete lattice"
},
{
"source": "Thesaurus:partially ordered set",
"word": "distributive lattice"
},
{
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"word": "Boolean lattice"
}
],
"lang": "English",
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"pos": "noun",
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{
"word": "complete partial order"
},
{
"word": "partial order"
}
],
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"A set that has a given, elsewhere specified partial order."
],
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"(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order."
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"text": "1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28,\nA partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of \"≻\" and speak of the partially ordered set P.\nThe ordered fields defined earlier are easily seen to be examples of partially ordered sets."
},
{
"ref": "1994, I. V. Evstigneev, P. E. Greenwood, Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting, American Mathematical Society, page 35",
"text": "In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set T_M.",
"type": "quotation"
},
{
"ref": "2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, page 45",
"text": "The invention of a derivative of a finite partially ordered set by Nazarova and Roiter in the late 1960s or early 1970s was a seminal event in the subject of representations of finite partially ordered sets (see [Simson 92]).",
"type": "quotation"
}
],
"glosses": [
"The ordered pair comprising a set and its partial order."
],
"links": [
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"(set theory, order theory, formally) The ordered pair comprising a set and its partial order."
],
"tags": [
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"topics": [
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"synonyms": [
{
"sense": "set on which a partial order is defined",
"word": "ground set"
},
{
"sense": "set on which a partial order is defined",
"word": "poset"
},
{
"sense": "ordered pair of set and partial order",
"word": "poset"
},
{
"source": "Thesaurus:partially ordered set",
"word": "partially ordered set"
}
],
"translations": [
{
"code": "ar",
"english": "Arabic Academy term",
"lang": "Arabic",
"roman": "fiʔatun murattabatun juzʔiyyan",
"sense": "set having a specified partial order",
"tags": [
"feminine"
],
"word": "فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
},
{
"code": "ar",
"lang": "Arabic",
"raw_tags": [
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],
"roman": "majmūʕatun murattabatun juzʔiyyan",
"sense": "set having a specified partial order",
"tags": [
"common",
"feminine"
],
"word": "مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
},
{
"code": "cs",
"lang": "Czech",
"sense": "set having a specified partial order",
"tags": [
"feminine"
],
"word": "uspořádaná množina"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "set having a specified partial order",
"word": "osittain järjestetty joukko"
},
{
"code": "de",
"lang": "German",
"sense": "set having a specified partial order",
"tags": [
"feminine"
],
"word": "partiell geordnete Menge"
},
{
"alt": "はんじゅんじょしゅうごう",
"code": "ja",
"lang": "Japanese",
"roman": "hanjunjo-shūgō",
"sense": "set having a specified partial order",
"word": "半順序集合"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "set having a specified partial order",
"tags": [
"common-gender"
],
"word": "partiellt ordnad mängd"
}
],
"wikipedia": [
"partially ordered set"
],
"word": "partially ordered set"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 using wiktextract (f4fd8c9 and c9440ce). 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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