See Cartesian product in All languages combined, or Wiktionary
{
"etymology_text": "From Cartesian + product, after French philosopher, mathematician, and scientist René Descartes (1596–1650), whose formulation of analytic geometry gave rise to the concept.",
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{
"_dis1": "39 21 29 11",
"sense": "set of possible pairs",
"word": "direct product"
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{
"_dis1": "39 21 29 11",
"code": "cmn",
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"sense": "set of possible pairs",
"word": "笛卡兒積"
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{
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"roman": "Díkǎ'ér jī",
"sense": "set of possible pairs",
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{
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"sense": "set of possible pairs",
"word": "Cartesiuse korrutis"
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"code": "et",
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"code": "et",
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"word": "ristikorrutis"
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"word": "karteesinen tulo"
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{
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"sense": "set of possible pairs",
"word": "tulojoukko"
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"_dis1": "39 21 29 11",
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"word": "produit cartésien"
},
{
"_dis1": "39 21 29 11",
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"sense": "set of possible pairs",
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"neuter"
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"word": "kartesisches Produkt"
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},
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"_dis1": "39 21 29 11",
"code": "el",
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"roman": "kartesianó ginómeno",
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"word": "καρτεσιανό γινόμενο"
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"_dis1": "39 21 29 11",
"code": "ja",
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{
"_dis1": "39 21 29 11",
"alt": "ちょくせきしゅうごう",
"code": "ja",
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}
],
"examples": [
{
"ref": "1997, Michel Marie Deza, Monique Laurent, Geometry of Cuts and Metrics, published 2009, page 297:",
"text": "The hypercube is the simplest example of a Cartesian product of graphs; indeed, the m-hypercube is nothing but (K₂)ᵐ.",
"type": "quote"
},
{
"ref": "2004, David Bao, Colleen Robles, “Ricci and Flag Curvatures in Finsler Geometry”, in David Dai-Wai Bao, Robert L. Bryant, Shiing-Shen Chern, Zhomgmin Shen, editors, A Sampler of Riemann-Finsler Geometry, page 246:",
"text": "A moment's thought convinces us of the following:\nThe Cartesian product of two Riemannian Einstein metrics with the same constant Ricci scalar ρ is again Ricci-constant, and has Ric",
"type": "quote"
}
],
"glosses": [
"Any of several generalizations of the set-theoretic sense, especially one which shares the geometrical intuition outlined above, i.e. one such that the product can be thought of as an object in its own right and not just as a set of pairs."
],
"id": "en-Cartesian_product-en-noun-zuEgeJTc",
"links": [
[
"mathematics",
"mathematics"
],
[
"generalization",
"generalization#English"
],
[
"intuition",
"intuition#English"
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],
"raw_glosses": [
"(mathematics) Any of several generalizations of the set-theoretic sense, especially one which shares the geometrical intuition outlined above, i.e. one such that the product can be thought of as an object in its own right and not just as a set of pairs."
],
"topics": [
"mathematics",
"sciences"
]
}
],
"wikipedia": [
"Cartesian product",
"René Descartes"
],
"word": "Cartesian product"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"Entries with translation boxes",
"Pages with 1 entry",
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"Terms with Estonian translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Greek translations",
"Terms with Italian translations",
"Terms with Japanese translations",
"Terms with Mandarin translations",
"Terms with Maori translations",
"Terms with Polish translations",
"Terms with Portuguese translations",
"Terms with Romanian translations",
"Terms with Russian translations",
"Terms with Serbo-Croatian translations",
"Terms with Spanish translations"
],
"etymology_text": "From Cartesian + product, after French philosopher, mathematician, and scientist René Descartes (1596–1650), whose formulation of analytic geometry gave rise to the concept.",
"forms": [
{
"form": "Cartesian products",
"tags": [
"plural"
]
}
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"args": {},
"expansion": "Cartesian product (plural Cartesian products)",
"name": "en-noun"
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"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"en:Set theory"
],
"glosses": [
"The set of all possible ordered pairs of elements, the being first from X, the second from Y, written X×Y. Formally, the set (x,y);|;x∈X;and;y∈Y."
],
"links": [
[
"set theory",
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[
"set",
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"ordered pair",
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"element",
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"raw_glosses": [
"(set theory, of two sets X and Y) The set of all possible ordered pairs of elements, the being first from X, the second from Y, written X×Y. Formally, the set (x,y);|;x∈X;and;y∈Y."
],
"raw_tags": [
"of two sets X and Y"
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"topics": [
"mathematics",
"sciences",
"set-theory"
]
},
{
"categories": [
"en:Databases"
],
"glosses": [
"All possible combinations of rows between all of the tables listed."
],
"links": [
[
"database",
"database"
],
[
"combination",
"combination"
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[
"row",
"row"
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[
"table",
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"raw_glosses": [
"(databases) All possible combinations of rows between all of the tables listed."
],
"topics": [
"computing",
"databases",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
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{
"categories": [
"English terms with quotations",
"en:Geometry"
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"examples": [
{
"ref": "1987, M. Göckeler, T. Schücker, Differential Geometry, Gauge Theories, and Gravity, published 1989, page 98:",
"text": "On the Cartesian product of two manifolds a differentiable structure can be constructed in the following way.",
"type": "quote"
}
],
"glosses": [
"An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from X and Y, but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. X and Y are vector spaces, the elements of X×Y are thought of as (m+n)-tuples instead of ordered pairs) and written X×Y."
],
"links": [
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"geometry",
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"raw_glosses": [
"(geometry, of an m-dimensional space X and an n-dimensional space Y) An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from X and Y, but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. X and Y are vector spaces, the elements of X×Y are thought of as (m+n)-tuples instead of ordered pairs) and written X×Y."
],
"raw_tags": [
"of an m-dimensional space X and an n-dimensional space Y"
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"topics": [
"geometry",
"mathematics",
"sciences"
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{
"categories": [
"English terms with quotations",
"en:Mathematics"
],
"examples": [
{
"ref": "1997, Michel Marie Deza, Monique Laurent, Geometry of Cuts and Metrics, published 2009, page 297:",
"text": "The hypercube is the simplest example of a Cartesian product of graphs; indeed, the m-hypercube is nothing but (K₂)ᵐ.",
"type": "quote"
},
{
"ref": "2004, David Bao, Colleen Robles, “Ricci and Flag Curvatures in Finsler Geometry”, in David Dai-Wai Bao, Robert L. Bryant, Shiing-Shen Chern, Zhomgmin Shen, editors, A Sampler of Riemann-Finsler Geometry, page 246:",
"text": "A moment's thought convinces us of the following:\nThe Cartesian product of two Riemannian Einstein metrics with the same constant Ricci scalar ρ is again Ricci-constant, and has Ric",
"type": "quote"
}
],
"glosses": [
"Any of several generalizations of the set-theoretic sense, especially one which shares the geometrical intuition outlined above, i.e. one such that the product can be thought of as an object in its own right and not just as a set of pairs."
],
"links": [
[
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"raw_glosses": [
"(mathematics) Any of several generalizations of the set-theoretic sense, especially one which shares the geometrical intuition outlined above, i.e. one such that the product can be thought of as an object in its own right and not just as a set of pairs."
],
"topics": [
"mathematics",
"sciences"
]
}
],
"synonyms": [
{
"sense": "set of possible pairs",
"word": "direct product"
},
{
"word": "cartesian product"
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "set of possible pairs",
"word": "笛卡兒積"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Díkǎ'ér jī",
"sense": "set of possible pairs",
"word": "笛卡儿积"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "set of possible pairs",
"word": "笛卡爾乘積"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Díkǎ'ěr chéngjī",
"sense": "set of possible pairs",
"word": "笛卡尔乘积"
},
{
"code": "cs",
"lang": "Czech",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "kartézský součin"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "cartesisch product"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "kruisproduct"
},
{
"code": "et",
"lang": "Estonian",
"sense": "set of possible pairs",
"word": "Cartesiuse korrutis"
},
{
"code": "et",
"lang": "Estonian",
"sense": "set of possible pairs",
"word": "otsekorrutis"
},
{
"code": "et",
"lang": "Estonian",
"sense": "set of possible pairs",
"word": "ristikorrutis"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "set of possible pairs",
"word": "karteesinen tulo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "set of possible pairs",
"word": "tulojoukko"
},
{
"code": "fr",
"lang": "French",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "produit cartésien"
},
{
"code": "de",
"lang": "German",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "kartesisches Produkt"
},
{
"code": "de",
"lang": "German",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "Kreuzprodukt"
},
{
"code": "el",
"lang": "Greek",
"roman": "kartesianó ginómeno",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "καρτεσιανό γινόμενο"
},
{
"code": "it",
"lang": "Italian",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "prodotto cartesiano"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "Dekaruto seki",
"sense": "set of possible pairs",
"word": "デカルト積"
},
{
"alt": "ちょくせきしゅうごう",
"code": "ja",
"english": "direct product",
"lang": "Japanese",
"roman": "chokuseki shūgō",
"sense": "set of possible pairs",
"word": "直積集合"
},
{
"code": "mi",
"lang": "Maori",
"sense": "set of possible pairs",
"word": "whātuinga takirua"
},
{
"code": "pl",
"lang": "Polish",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "iloczyn kartezjański"
},
{
"code": "pl",
"lang": "Polish",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "produkt kartezjański"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "produto cartesiano"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "produs cartezian"
},
{
"code": "ru",
"lang": "Russian",
"roman": "dɛkártovo proizvedénije",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "дека́ртово произведе́ние"
},
{
"code": "ru",
"english": "direct product",
"lang": "Russian",
"roman": "prjamóje proizvedénije",
"sense": "set of possible pairs",
"tags": [
"neuter"
],
"word": "прямо́е произведе́ние"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "Kartezijev produkt"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of possible pairs",
"tags": [
"masculine"
],
"word": "producto cartesiano"
}
],
"wikipedia": [
"Cartesian product",
"René Descartes"
],
"word": "Cartesian product"
}
Download raw JSONL data for Cartesian product meaning in English (8.6kB)
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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 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.