0Continuity And Differentiability : Bernard Bolzano first given the definition of continuity in 1817, after this Augustin-Louis Cauchy Defined continuity as an infinitely small increment of the independent variable x in y = f ( x ) always leads to infinitely small change in dependent variable y . Here infinite small quantities were defined in terms of variable quantities and this definition of continuity closely parallels the infinitesimal definition used today.
