epsilontic
English
[edit]Etymology
[edit](This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium. Particularly: “Was this borrowed from some other language? Why not "epsilonic"?”) From the fact that ε is the usual symbol used to denote an error bound.
Adjective
[edit]epsilontic
- (mathematics) Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals.
- 1966, J. C. Oxtoby, B. J. Pettis, G. B. Price, John Von Neumann, 1903-1957, American Mathematical Soc., →ISBN, page 88:
- 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.
- 1969, J. M. Ziman, Elements of Advanced Quantum Theory, Cambridge University Press, →ISBN, page 238:
- 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)
- 1996, Ronald Calinger, Vita Mathematica: Historical Research and Integration with Teaching, Cambridge University Press, →ISBN, page 168:
- 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.
- 2009, Detlef Laugwitz, Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Springer Science & Business Media, →ISBN, page 44:
- 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.
Derived terms
[edit]Translations
[edit]pertaining to epsilon-delta analysis