英和和英

形容詞

epsilontic

1. (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 9780821896792), 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 9780521099493), 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 9780883850978), 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 9780817647773), 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.

派生語

• epsilontics