without loss of generality

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

Synonyms

• w.l.o.g., wlog (abbreviation)

Translations

without loss of generality

Danish: uden tab af generalitet Dutch: zonder verlies van algemeenheid (z.v.v.a.) 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) Romanian: fără a reduce generalitatea Spanish: sin pérdida de generalidad