See ordered pair on Wiktionary
{
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"form": "ordered pairs",
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{
"kind": "topical",
"langcode": "en",
"name": "Set theory",
"orig": "en:Set theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"text": "If an ordered pair were defined (in terms of sets) as (x,y):=a,a,b then the \"first element\" of an ordered pair S could be defined as CAR(S) where CAR(S) = x if and only if (∀y∈S.,x∈y). Likewise, the \"second element\" of S could be defined as CDR(S) where CDR(S) = x if and only if (∃y∈S.,(∃z∈y.,x∈z)). If the two elements happened to be equal, then the ordered pair would still have cardinality two as would be naturally expected."
}
],
"glosses": [
"An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or ⟨a,b⟩."
],
"id": "en-ordered_pair-en-noun-zqpm6OGD",
"links": [
[
"set theory",
"set theory"
],
[
"element",
"element"
]
],
"raw_glosses": [
"(set theory) An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or ⟨a,b⟩."
],
"related": [
{
"word": "triple"
},
{
"word": "triplet"
},
{
"word": "tuple"
}
],
"topics": [
"mathematics",
"sciences",
"set-theory"
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "in set theory",
"word": "有序對"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yǒuxùduì",
"sense": "in set theory",
"word": "有序对"
},
{
"code": "cs",
"lang": "Czech",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "uspořádaná dvojice"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "in set theory",
"word": "järjestetty pari"
},
{
"code": "fr",
"lang": "French",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "couple"
},
{
"code": "gl",
"lang": "Galician",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "par ordenado"
},
{
"code": "de",
"lang": "German",
"sense": "in set theory",
"tags": [
"neuter"
],
"word": "geordnetes Paar"
},
{
"code": "el",
"lang": "Greek",
"roman": "diatetagméno zévgos",
"sense": "in set theory",
"tags": [
"neuter"
],
"word": "διατεταγμένο ζεύγος"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "in set theory",
"word": "rendezett pár"
},
{
"code": "it",
"lang": "Italian",
"sense": "in set theory",
"word": "coppia"
},
{
"code": "it",
"lang": "Italian",
"sense": "in set theory",
"word": "coppia ordinata"
},
{
"alt": "じゅんじょつい",
"code": "ja",
"lang": "Japanese",
"roman": "junjo-tsui",
"sense": "in set theory",
"word": "順序対"
},
{
"code": "ko",
"lang": "Korean",
"roman": "sunseossang",
"sense": "in set theory",
"word": "순서쌍"
},
{
"code": "mi",
"lang": "Maori",
"sense": "in set theory",
"word": "takirua raupapa"
},
{
"code": "pl",
"lang": "Polish",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "para uporządkowana"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "par ordenado"
},
{
"code": "ru",
"lang": "Russian",
"roman": "uporjádočennaja pára",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "упоря́доченная па́ра"
},
{
"code": "ru",
"lang": "Russian",
"roman": "pára",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "па́ра"
},
{
"code": "es",
"lang": "Spanish",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "par ordenado"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "in set theory",
"word": "ordnat par"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "in set theory",
"word": "kapid na ayos"
}
],
"wikipedia": [
"ordered pair"
]
}
],
"word": "ordered pair"
}
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"pos": "noun",
"related": [
{
"word": "triple"
},
{
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{
"text": "If an ordered pair were defined (in terms of sets) as (x,y):=a,a,b then the \"first element\" of an ordered pair S could be defined as CAR(S) where CAR(S) = x if and only if (∀y∈S.,x∈y). Likewise, the \"second element\" of S could be defined as CDR(S) where CDR(S) = x if and only if (∃y∈S.,(∃z∈y.,x∈z)). If the two elements happened to be equal, then the ordered pair would still have cardinality two as would be naturally expected."
}
],
"glosses": [
"An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or ⟨a,b⟩."
],
"links": [
[
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"(set theory) An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or ⟨a,b⟩."
],
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"mathematics",
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "in set theory",
"word": "有序對"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yǒuxùduì",
"sense": "in set theory",
"word": "有序对"
},
{
"code": "cs",
"lang": "Czech",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "uspořádaná dvojice"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "in set theory",
"word": "järjestetty pari"
},
{
"code": "fr",
"lang": "French",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "couple"
},
{
"code": "gl",
"lang": "Galician",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "par ordenado"
},
{
"code": "de",
"lang": "German",
"sense": "in set theory",
"tags": [
"neuter"
],
"word": "geordnetes Paar"
},
{
"code": "el",
"lang": "Greek",
"roman": "diatetagméno zévgos",
"sense": "in set theory",
"tags": [
"neuter"
],
"word": "διατεταγμένο ζεύγος"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "in set theory",
"word": "rendezett pár"
},
{
"code": "it",
"lang": "Italian",
"sense": "in set theory",
"word": "coppia"
},
{
"code": "it",
"lang": "Italian",
"sense": "in set theory",
"word": "coppia ordinata"
},
{
"alt": "じゅんじょつい",
"code": "ja",
"lang": "Japanese",
"roman": "junjo-tsui",
"sense": "in set theory",
"word": "順序対"
},
{
"code": "ko",
"lang": "Korean",
"roman": "sunseossang",
"sense": "in set theory",
"word": "순서쌍"
},
{
"code": "mi",
"lang": "Maori",
"sense": "in set theory",
"word": "takirua raupapa"
},
{
"code": "pl",
"lang": "Polish",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "para uporządkowana"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "par ordenado"
},
{
"code": "ru",
"lang": "Russian",
"roman": "uporjádočennaja pára",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "упоря́доченная па́ра"
},
{
"code": "ru",
"lang": "Russian",
"roman": "pára",
"sense": "in set theory",
"tags": [
"feminine"
],
"word": "па́ра"
},
{
"code": "es",
"lang": "Spanish",
"sense": "in set theory",
"tags": [
"masculine"
],
"word": "par ordenado"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "in set theory",
"word": "ordnat par"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "in set theory",
"word": "kapid na ayos"
}
],
"word": "ordered pair"
}
Download raw JSONL data for ordered pair meaning in All languages combined (4.5kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 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.