without loss of generality

English

Prepositional phrase

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.

   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 $x^{2}+y^{2}=1$.

Synonyms

• w.l.o.g., wlog, wolog (all abbreviations)

Translations

without loss of generality

• Chinese:

  Mandarin: 不失一般性 (bùshī yībānxìng)

• Danish: uden tab af generalitet
• Dutch: zonder verlies van algemeenheid (z.v.v.a.)
• Finnish: yleisyyttä menettämättä
• French: sans perte de généralité (fr)
• Georgian: ზოგადობის შეუზღუდავად (zogadobis šeuzɣudavad)
• German: ohne Beschränkung der Allgemeinheit, o. B. d. A. (de), o. E.
• Hebrew: בלי הגבלת הכלליות (blí hagbalát haklaliút), בה"כ (he)
• Hungarian: az általánosság elvesztése nélkül
• Romanian: fără a reduce generalitatea
• Russian: без потери общности (bez poteri obščnosti), не теряя общности (ne terjaja obščnosti)
• Spanish: sin pérdida de generalidad