(ε, δ)-definition of limit

In calculus, the (ε, δ)-definition of limit ("epsilon-delta definition of limit") is a formalization of the notion of limit. It was first given by Bernard Bolzano in 1817, and the definitive modern statement was ultimately provided by Karl Weierstrass. It makes rigorous the following informal notion: the dependent expression f(x) approaches the value L as the variable x approaches the value c if f(x) can be made as close as desired to L by taking x sufficiently close to c.