See partial order in All languages combined, or Wiktionary
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"text": "1986, Kenneth R. Goodearl, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, Softcover reprint 2010, page xxi,\nA partial order on a set X is any reflexive, antisymmetric, transitive relation on X. In most cases, partial orders are denoted ≤."
},
{
"text": "1999, Paul A. S. Ward, An Online Algorithm for Dimension-Bound Analysis, Patrick Amestoy, P. Berger, M. Daydé, I. Duff, V. Frayssé, L. Giraud, D. Ruiz (editors), Euro-Par ’99 Parallel Processing: 5th International Euro-Par Conference, Proceedings, Springer, LNCS 1685, page 144,\nThe vector-clock size necessary to characterize causality in a distributed computation is bounded by the dimension of the partial order induced by that computation."
},
{
"ref": "2008, David Eppstein, Jean-Claude Falmagne, Sergei Ovchinnikov, Media Theory: Interdisciplinary Applied Mathematics, Springer, page 7:",
"text": "Consider an arbitrary finite set S. The family #x5C;mathcal#x7B;P#x7D; of all strict partial orders (asymmetric, transitive, cf. 1.8.3, p. 14) on S enjoys a remarkable property: any partial order P can be linked to any other partial order P’ by a sequence of steps each of which consists of changing the order either by adding one ordered pair of elements of S (imposing an ordering between two previously-incomparable elements) or by removing one ordered pair (causing two previously related elements to become incomparable), without ever leaving the family #x5C;mathcal#x7B;P#x7D;.",
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"(informal) An ordering of the elements of a collection that behaves like that of the natural numbers by size, except that some elements may not be comparable (if all elements are comparable, it is called a total order); (formal) a binary relation that is reflexive, antisymmetric, and transitive."
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"(set theory, order theory) (informal) An ordering of the elements of a collection that behaves like that of the natural numbers by size, except that some elements may not be comparable (if all elements are comparable, it is called a total order); (formal) a binary relation that is reflexive, antisymmetric, and transitive."
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"synonyms": [
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"translations": [
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"code": "cs",
"lang": "Czech",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"tags": [
"neuter"
],
"word": "uspořádání"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "osittainen järjestys"
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"code": "fi",
"lang": "Finnish",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "osittaisjärjestys"
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
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"word": "Halbordnung"
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"code": "de",
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
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"word": "partielle Ordnung"
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"alt": "はんじゅんじょ",
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "부분 순서"
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"lang": "Russian",
"roman": "častíčnyj porjádok",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "части́чный поря́док"
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "partiell ordning"
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"word": "partial order"
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"text": "1986, Kenneth R. Goodearl, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, Softcover reprint 2010, page xxi,\nA partial order on a set X is any reflexive, antisymmetric, transitive relation on X. In most cases, partial orders are denoted ≤."
},
{
"text": "1999, Paul A. S. Ward, An Online Algorithm for Dimension-Bound Analysis, Patrick Amestoy, P. Berger, M. Daydé, I. Duff, V. Frayssé, L. Giraud, D. Ruiz (editors), Euro-Par ’99 Parallel Processing: 5th International Euro-Par Conference, Proceedings, Springer, LNCS 1685, page 144,\nThe vector-clock size necessary to characterize causality in a distributed computation is bounded by the dimension of the partial order induced by that computation."
},
{
"ref": "2008, David Eppstein, Jean-Claude Falmagne, Sergei Ovchinnikov, Media Theory: Interdisciplinary Applied Mathematics, Springer, page 7:",
"text": "Consider an arbitrary finite set S. The family #x5C;mathcal#x7B;P#x7D; of all strict partial orders (asymmetric, transitive, cf. 1.8.3, p. 14) on S enjoys a remarkable property: any partial order P can be linked to any other partial order P’ by a sequence of steps each of which consists of changing the order either by adding one ordered pair of elements of S (imposing an ordering between two previously-incomparable elements) or by removing one ordered pair (causing two previously related elements to become incomparable), without ever leaving the family #x5C;mathcal#x7B;P#x7D;.",
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"(informal) An ordering of the elements of a collection that behaves like that of the natural numbers by size, except that some elements may not be comparable (if all elements are comparable, it is called a total order); (formal) a binary relation that is reflexive, antisymmetric, and transitive."
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"(set theory, order theory) (informal) An ordering of the elements of a collection that behaves like that of the natural numbers by size, except that some elements may not be comparable (if all elements are comparable, it is called a total order); (formal) a binary relation that is reflexive, antisymmetric, and transitive."
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"code": "cs",
"lang": "Czech",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"tags": [
"neuter"
],
"word": "uspořádání"
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "osittainen järjestys"
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"code": "fi",
"lang": "Finnish",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "osittaisjärjestys"
},
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
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"word": "Halbordnung"
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"code": "de",
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"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"tags": [
"feminine"
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"word": "partielle Ordnung"
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{
"alt": "はんじゅんじょ",
"code": "ja",
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"roman": "hanjunjo",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "半順序"
},
{
"code": "ko",
"lang": "Korean",
"roman": "bubun sunseo",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "부분 순서"
},
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"code": "ru",
"lang": "Russian",
"roman": "častíčnyj porjádok",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "части́чный поря́док"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "partiell ordning"
}
],
"word": "partial order"
}
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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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