On the history of epsilontics

TL;DR

This paper reviews the historical development of epsilon-delta notation in 19th-century mathematics, highlighting key contributions and clarifying the evolution of the concept from Cauchy to Weierstrass.

Contribution

It provides a detailed historical analysis of epsilon-delta language, emphasizing the lack of a functional relationship in early definitions and tracing its formalization.

Findings

Cauchy introduced epsilon and delta symbols in 1823 without a functional relationship.

Weierstrass' 1861 definition fully formalized the epsilon-delta method.

Historical interpretations clarify the conceptual evolution of limits in analysis.

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.