# without loss of generality

## English

### Prepositional phrase

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