"without loss of generality" meaning in English

See without loss of generality in All languages combined, or Wiktionary

Prepositional phrase

Head templates: {{head|en|prepositional phrase|head=}} without loss of generality, {{en-PP}} without loss of generality
  1. (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. Wikipedia link: without loss of generality Categories (topical): Mathematics Synonyms: w.l.o.g., wlog, wolog [abbreviation] Translations (without loss of generality): 不失一般性 (bùshī yībānxìng) (Chinese Mandarin), uden tab af generalitet (Danish), zonder verlies van algemeenheid (z.v.v.a.) (Dutch), yleisyyttä menettämättä (Finnish), sans perte de généralité (French), ზოგადობის შეუზღუდავად (zogadobis šeuzɣudavad) (Georgian), ohne Beschränkung der Allgemeinheit (German), o. B. d. A. (German), o. E. (German), בלי הגבלת הכלליות (blí hagbalát haklaliút) (Hebrew), בה"כ (Hebrew), az általánosság elvesztése nélkül (Hungarian), fără a reduce generalitatea (Romanian), без потери общности (bez poteri obščnosti) (Russian), не теряя общности (ne terjaja obščnosti) (Russian), sin pérdida de generalidad (Spanish)

Alternative forms

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          "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#x2B;y²#x3D;1.",
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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."
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          "word": "w.l.o.g."
        },
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          "word": "wlog"
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          "tags": [
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        {
          "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"
        },
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          "code": "de",
          "lang": "German",
          "sense": "without loss of generality",
          "word": "ohne Beschränkung der Allgemeinheit"
        },
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          "code": "de",
          "lang": "German",
          "sense": "without loss of generality",
          "word": "o. B. d. A."
        },
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          "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"
        },
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          "lang": "Hungarian",
          "sense": "without loss of generality",
          "word": "az általánosság elvesztése nélkül"
        },
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          "lang": "Romanian",
          "sense": "without loss of generality",
          "word": "fără a reduce generalitatea"
        },
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          "lang": "Russian",
          "roman": "bez poteri obščnosti",
          "sense": "without loss of generality",
          "word": "без потери общности"
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          "lang": "Russian",
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          "sense": "without loss of generality",
          "word": "не теряя общности"
        },
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          "lang": "Spanish",
          "sense": "without loss of generality",
          "word": "sin pérdida de generalidad"
        }
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        "without loss of generality"
      ]
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      "code": "cmn",
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      "roman": "bùshī yībānxìng",
      "sense": "without loss of generality",
      "word": "不失一般性"
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      "sense": "without loss of generality",
      "word": "uden tab af generalitet"
    },
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      "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"
    },
    {
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      "lang": "German",
      "sense": "without loss of generality",
      "word": "o. B. d. A."
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      "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": "ru",
      "lang": "Russian",
      "roman": "bez poteri obščnosti",
      "sense": "without loss of generality",
      "word": "без потери общности"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "ne terjaja obščnosti",
      "sense": "without loss of generality",
      "word": "не теряя общности"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "without loss of generality",
      "word": "sin pérdida de generalidad"
    }
  ],
  "word": "without loss of generality"
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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 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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.

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