See without loss of generality in All languages combined, or Wiktionary
Download JSON data for without loss of generality meaning in English (3.6kB)
{
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"expansion": "without loss of generality",
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"lang": "English",
"lang_code": "en",
"pos": "prep_phrase",
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"categories": [
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"kind": "other",
"name": "English entries with incorrect language header",
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{
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"parents": [
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"source": "w"
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{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
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"Sciences",
"All topics",
"Fundamental"
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"source": "w"
}
],
"examples": [
{
"text": "We wish to prove two ellipses in the plane intersect in an even number of points or are tangent. Without loss of generality, assume one of them has the equation x²+y²=1."
}
],
"glosses": [
"With a constraining assumption that, however, makes it clear how to apply the proof performed under this assumption to the general case unconstrained by the assumption."
],
"id": "en-without_loss_of_generality-en-prep_phrase-sw0z3Yhy",
"links": [
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"raw_glosses": [
"(mathematics) With a constraining assumption that, however, makes it clear how to apply the proof performed under this assumption to the general case unconstrained by the assumption."
],
"synonyms": [
{
"word": "w.l.o.g."
},
{
"word": "wlog"
},
{
"tags": [
"abbreviation"
],
"word": "wolog"
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"topics": [
"mathematics",
"sciences"
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "bùshī yībānxìng",
"sense": "without loss of generality",
"word": "不失一般性"
},
{
"code": "da",
"lang": "Danish",
"sense": "without loss of generality",
"word": "uden tab af generalitet"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "without loss of generality",
"word": "zonder verlies van algemeenheid (z.v.v.a.)"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "without loss of generality",
"word": "yleisyyttä menettämättä"
},
{
"code": "fr",
"lang": "French",
"sense": "without loss of generality",
"word": "sans perte de généralité"
},
{
"code": "ka",
"lang": "Georgian",
"roman": "zogadobis šeuzɣudavad",
"sense": "without loss of generality",
"word": "ზოგადობის შეუზღუდავად"
},
{
"code": "de",
"lang": "German",
"sense": "without loss of generality",
"word": "ohne Beschränkung der Allgemeinheit"
},
{
"code": "de",
"lang": "German",
"sense": "without loss of generality",
"word": "o. B. d. A."
},
{
"code": "de",
"lang": "German",
"sense": "without loss of generality",
"word": "o. E."
},
{
"code": "he",
"lang": "Hebrew",
"roman": "blí hagbalát haklaliút",
"sense": "without loss of generality",
"word": "בלי הגבלת הכלליות"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "without loss of generality",
"word": "בה\"כ"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "without loss of generality",
"word": "az általánosság elvesztése nélkül"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "without loss of generality",
"word": "fără a reduce generalitatea"
},
{
"code": "es",
"lang": "Spanish",
"sense": "without loss of generality",
"word": "sin pérdida de generalidad"
}
],
"wikipedia": [
"without loss of generality"
]
}
],
"word": "without loss of generality"
}
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"expansion": "without loss of generality",
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"expansion": "without loss of generality",
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"lang": "English",
"lang_code": "en",
"pos": "prep_phrase",
"senses": [
{
"categories": [
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"English multiword terms",
"English prepositional phrases",
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"examples": [
{
"text": "We wish to prove two ellipses in the plane intersect in an even number of points or are tangent. Without loss of generality, assume one of them has the equation x²+y²=1."
}
],
"glosses": [
"With a constraining assumption that, however, makes it clear how to apply the proof performed under this assumption to the general case unconstrained by the assumption."
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"(mathematics) With a constraining assumption that, however, makes it clear how to apply the proof performed under this assumption to the general case unconstrained by the assumption."
],
"topics": [
"mathematics",
"sciences"
],
"wikipedia": [
"without loss of generality"
]
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"synonyms": [
{
"word": "w.l.o.g."
},
{
"word": "wlog"
},
{
"tags": [
"abbreviation"
],
"word": "wolog"
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "bùshī yībānxìng",
"sense": "without loss of generality",
"word": "不失一般性"
},
{
"code": "da",
"lang": "Danish",
"sense": "without loss of generality",
"word": "uden tab af generalitet"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "without loss of generality",
"word": "zonder verlies van algemeenheid (z.v.v.a.)"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "without loss of generality",
"word": "yleisyyttä menettämättä"
},
{
"code": "fr",
"lang": "French",
"sense": "without loss of generality",
"word": "sans perte de généralité"
},
{
"code": "ka",
"lang": "Georgian",
"roman": "zogadobis šeuzɣudavad",
"sense": "without loss of generality",
"word": "ზოგადობის შეუზღუდავად"
},
{
"code": "de",
"lang": "German",
"sense": "without loss of generality",
"word": "ohne Beschränkung der Allgemeinheit"
},
{
"code": "de",
"lang": "German",
"sense": "without loss of generality",
"word": "o. B. d. A."
},
{
"code": "de",
"lang": "German",
"sense": "without loss of generality",
"word": "o. E."
},
{
"code": "he",
"lang": "Hebrew",
"roman": "blí hagbalát haklaliút",
"sense": "without loss of generality",
"word": "בלי הגבלת הכלליות"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "without loss of generality",
"word": "בה\"כ"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "without loss of generality",
"word": "az általánosság elvesztése nélkül"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "without loss of generality",
"word": "fără a reduce generalitatea"
},
{
"code": "es",
"lang": "Spanish",
"sense": "without loss of generality",
"word": "sin pérdida de generalidad"
}
],
"word": "without loss of generality"
}
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.