On the history of epsilontics

Abstract

This is a overview of the genesis of epsilon-delta language in works of mathematicians of the 19th century. It shows that although the symbols epsilon and delta were initially introduced in 1823 by Cauchy, no functional relationship for delta as a function of epsilon was ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass' definition of a limit. The article gives various interpretations of these issues later provided by mathematicians.