without loss of generality

Prepositional phrase

 * 1)  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 $$x^2+y^2=1$$.

Translations

 * Chinese:
 * Mandarin: 不失一般性
 * Danish: uden tab af generalitet
 * Dutch: zonder verlies van algemeenheid (z.v.v.a.)
 * Finnish: yleisyyttä menettämättä
 * French:
 * Georgian: ზოგადობის შეუზღუდავად
 * German: ohne Beschränkung der Allgemeinheit,, o. E.
 * Hebrew: בלי הגבלת הכלליות,
 * Hungarian: az általánosság elvesztése nélkül
 * Romanian: fără a reduce generalitatea
 * Spanish: sin pérdida de generalidad