See partial order in All languages combined, or Wiktionary
Download JSON data for partial order meaning in English (5.0kB)
{
"forms": [
{
"form": "partial orders",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "partial order (plural partial orders)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Japanese terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Set theory",
"orig": "en:Set theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"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;.",
"type": "quotation"
}
],
"glosses": [
"(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."
],
"hypernyms": [
{
"word": "preorder"
}
],
"hyponyms": [
{
"sense": "total order",
"word": "well-order"
}
],
"id": "en-partial_order-en-noun-0ZG03QHM",
"links": [
[
"set theory",
"set theory"
],
[
"ordering",
"order"
],
[
"element",
"element"
],
[
"collection",
"collection"
],
[
"natural number",
"natural number"
],
[
"comparable",
"comparable"
],
[
"total order",
"total order"
],
[
"binary relation",
"binary relation"
],
[
"reflexive",
"reflexive"
],
[
"antisymmetric",
"antisymmetric"
],
[
"transitive",
"transitive"
]
],
"raw_glosses": [
"(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."
],
"related": [
{
"word": "order"
},
{
"word": "partially ordered set"
}
],
"synonyms": [
{
"word": "partial ordering relation"
}
],
"topics": [
"mathematics",
"order-theory",
"sciences",
"set-theory"
],
"translations": [
{
"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"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "osittaisjärjestys"
},
{
"code": "de",
"lang": "German",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"tags": [
"feminine"
],
"word": "Halbordnung"
},
{
"code": "de",
"lang": "German",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"tags": [
"feminine"
],
"word": "partielle Ordnung"
},
{
"alt": "はんじゅんじょ",
"code": "ja",
"lang": "Japanese",
"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"
},
{
"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"
}
{
"forms": [
{
"form": "partial orders",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "partial order (plural partial orders)",
"name": "en-noun"
}
],
"hypernyms": [
{
"word": "preorder"
}
],
"hyponyms": [
{
"sense": "total order",
"word": "well-order"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "order"
},
{
"word": "partially ordered set"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English formal terms",
"English informal terms",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"Japanese terms with redundant script codes",
"en:Set theory"
],
"examples": [
{
"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;.",
"type": "quotation"
}
],
"glosses": [
"(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."
],
"links": [
[
"set theory",
"set theory"
],
[
"ordering",
"order"
],
[
"element",
"element"
],
[
"collection",
"collection"
],
[
"natural number",
"natural number"
],
[
"comparable",
"comparable"
],
[
"total order",
"total order"
],
[
"binary relation",
"binary relation"
],
[
"reflexive",
"reflexive"
],
[
"antisymmetric",
"antisymmetric"
],
[
"transitive",
"transitive"
]
],
"raw_glosses": [
"(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."
],
"topics": [
"mathematics",
"order-theory",
"sciences",
"set-theory"
]
}
],
"synonyms": [
{
"word": "partial ordering relation"
}
],
"translations": [
{
"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"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"word": "osittaisjärjestys"
},
{
"code": "de",
"lang": "German",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"tags": [
"feminine"
],
"word": "Halbordnung"
},
{
"code": "de",
"lang": "German",
"sense": "binary relation that is reflexive, antisymmetric, and transitive",
"tags": [
"feminine"
],
"word": "partielle Ordnung"
},
{
"alt": "はんじゅんじょ",
"code": "ja",
"lang": "Japanese",
"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"
},
{
"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"
}
This page is a part of the kaikki.org machine-readable English 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.