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