The insight of Bolzano and Cauchy was to define a general notion of continuity (in terms of infinitesimals in Cauchy's case and using real inequalities in Bolzano's case), and to provide a proof based on such definitions.
Uvid Bolzana i Cauchya je bio definiranje općenitog koncepta neprekidnosti (preko infinitezimalnih veličina u Cauchyevom slučaju i koristeći nejednakosti u Bolzanovom slučaju), i davanje dokaza baziranog na takvim definicijama.