page_title: (ε, δ)-definition of limit
hierarchical_section_title: (ε, δ)-definition of limit
context_page_description: In calculus, the-definition of limit is a formalization of the notion of limit. The concept is due to Augustin-Louis Cauchy, who never gave an definition of limit in his Cours d'Analyse, but occasionally used arguments in proofs. It was first given as a formal definition by Bernard Bolzano in 1817, and the definitive modern statement was ultimately provided by Karl Weierstrass. It provides rigor to 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.
context_section_description: In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit. The concept is due to Augustin-Louis Cauchy, who never gave an () definition of limit in his Cours d'Analyse, but occasionally used  arguments in proofs. It was first given as a formal definition by Bernard Bolzano in 1817, and the definitive modern statement was ultimately provided by Karl Weierstrass. It provides rigor to 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.
caption: Whenever a point x is within δ units of c, f(x) is within ε units of L