See ordered field on Wiktionary
{
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"form": "ordered fields",
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"glosses": [
"A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
],
"hypernyms": [
{
"word": "field"
},
{
"word": "ordered integral domain"
}
],
"hyponyms": [
{
"sense": "Archimedean ordered field",
"word": "real number system"
},
{
"word": "Euclidean field"
}
],
"id": "en-ordered_field-en-noun-uHb1zqTJ",
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[
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[
"order relation",
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[
"trichotomy",
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],
[
"transitivity",
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],
"raw_glosses": [
"(algebra) A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
],
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"translations": [
{
"code": "pt",
"lang": "Portuguese",
"sense": "field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides",
"tags": [
"masculine"
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"word": "corpo ordenado"
},
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"sense": "field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides",
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"word": "corp ordonat"
}
]
}
],
"word": "ordered field"
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"A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
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"algebra",
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"(algebra) A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
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"lang": "Portuguese",
"sense": "field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides",
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"word": "corpo ordenado"
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"word": "corp ordonat"
}
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"word": "ordered field"
}
Download raw JSONL data for ordered field meaning in All languages combined (2.0kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 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.
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.