Meaning of epsilontic | Babel Free

Definitions

Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals.

Examples

“The question⟳ is of a technical, gymnastic kind, and von Neumann's positive answer⟳ [4] uses the set-theoretic and epsilontic trickery appropriate to this domain.”

“If a parameter such as x in (7.71) is continuous, there are other operations of the group 'as close⟳ as one likes' to any given operation; in 'epsilontic' language, we must be able to write⟳ T(x + ε) → T(x) as ε → 0. (7.76)”

“Weierstrass precisely defines a function in the modern sense⟳ as a correspondence between two variable quantities—a definition he attributes to Fourier, Cauchy, and Dirichlet—and develops the epsilontic method.”

“Riemann definitely accepts the epsilontic justification of limit⟳ analysis, as shown by his well-known introduction of the concept of the integral in his habilitation paper of 1853 (W. 239), and, more fully, by this paper as a whole.”

CEFR level