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epsilonic
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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 ( * * * * ε * , * δ * * * {\displaystyle \varepsilon ,\delta } * ) definition of limit in his Cours d'Analyse, but occasionally used * * * * ε * , * δ * * * {\displaystyle \varepsilon ,\delta } * 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 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. |