without loss of generality

prepositional phrase

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.

“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#43;y²#61;1.”

Similar
w.l.o.g.wlogwolog
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Meanings

prepositional phrase
  1. mathematicsWith 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.

    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#43;y²#61;1.

    Synonyms: w.l.o.g., wlog, wolog, W.L.O.G., WLOG, WOLOG

Synonyms & antonyms

prepositional phraseWith 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.

Similar
w.l.o.g.wlogwologW.L.O.G.WLOGWOLOG

Translations

Chinese Mandarin 不失一般性
  • 不失一般性 (bùshī yībānxìng)without loss of generality
Czech bez újmy na obecnosti
  • bez újmy na obecnostiwithout loss of generality
Danish uden tab af generalitet
  • uden tab af generalitetwithout loss of generality
Dutch zonder verlies van algemeenheid (z.v.v.a.)
  • zonder verlies van algemeenheid (z.v.v.a.)without loss of generality
Finnish yleisyyttä menettämättä
  • yleisyyttä menettämättäwithout loss of generality
French sans perte de généralité
  • sans perte de généralitéwithout loss of generality
German ohne Beschränkung der Allgemeinheit
  • ohne Beschränkung der Allgemeinheitwithout loss of generality
Hebrew בלי הגבלת הכלליות, בה״כ
  • בלי הגבלת הכלליות (blí hagbalát haklaliút)without loss of generality
  • בה״כwithout loss of generality
Hungarian az általánosság elvesztése nélkül
  • az általánosság elvesztése nélkülwithout loss of generality
Indonesian tanpa mengurangi keumuman
  • tanpa mengurangi keumumanwithout loss of generality
Romanian fără a reduce generalitatea
  • fără a reduce generalitateawithout loss of generality
Russian без потери общности, не теряя общности
  • без потери общности (bez poteri obščnosti)without loss of generality
  • не теряя общности (ne terjaja obščnosti)without loss of generality
Spanish sin pérdida de generalidad
  • sin pérdida de generalidadwithout loss of generality
Cite this entry
APA

without loss of generality. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/without%20loss%20of%20generality

MLA

“without loss of generality.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/without%20loss%20of%20generality. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “without loss of generality,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/without%20loss%20of%20generality.

Source: without loss of generality on Wiktionary, CC BY-SA 4.0.