"epsilontics" meaning in All languages combined

See epsilontics on Wiktionary

Noun [English]

Head templates: {{en-noun|p}} epsilontics pl (plural only)
  1. (mathematics) An approach to mathematical analysis using the epsilon-delta definition of a limit, i.e. with explicit estimation of error bounds, as opposed to using infinitesimals. Tags: plural, plural-only Categories (topical): Mathematics
    Sense id: en-epsilontics-en-noun-lc1GdRua Categories (other): English entries with incorrect language header, English pluralia tantum Disambiguation of English entries with incorrect language header: 67 33 Disambiguation of English pluralia tantum: 66 34 Topics: mathematics, sciences
  2. (mathematics) An instance of reasoning performed using this approach. Tags: plural, plural-only Categories (topical): Mathematics
    Sense id: en-epsilontics-en-noun-QEtk3g6c Topics: mathematics, sciences

Download JSON data for epsilontics meaning in All languages combined (4.7kB)

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        {
          "ref": "1973, Hans Freudenthal, Mathematics as an Educational Task, Springer Science & Business Media, page 148",
          "text": "Now epsilontics is losing ground, and after one or two decennia we can expect the \"great discovery\" that, properly understood, the infinitesimal methods of a century ago are completely rigorous. Algorithms with differentials are already modern.",
          "type": "quotation"
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          "ref": "1981, John M. Ziman, Puzzles, Problems and Enigmas: Occasional Pieces on the Human Aspects of Science, Cambridge University Press, page 51",
          "text": "In principle, we should not then have made any approximation at all; it is a rule of pure mathematics, hallowed by centuries of usage, and justified by the mysteries known to undergraduates as 'epsilontics', that a convergent series is as good as a simple finite algebraic expression for a solution — which is just as well, because almost every expression that appears in any formula in physics, such as a cosine, or a logarithm, is itself only definable algebraically as the sum of an infinite series.",
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          "ref": "2009, Detlef Laugwitz, Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Springer Science & Business Media, page 59",
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        "(mathematics) An approach to mathematical analysis using the epsilon-delta definition of a limit, i.e. with explicit estimation of error bounds, as opposed to using infinitesimals."
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          "ref": "1999, Roland Omnès, Understanding Quantum Mechanics, Princeton University Press, page 185",
          "text": "One might be more precise by giving an error for equation (16.2) or by considering the much smaller errors on the exclusion of other classical properties, but these epsilontics will be omitted.",
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        {
          "ref": "2001, Peter Schuster, Ulrich Berger, Horst Osswald, Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum, Springer Science & Business Media, page 137",
          "text": "Thus, Hadamard avoids Weierstrassian epsilontics in his text for engineering students.",
          "type": "quotation"
        },
        {
          "ref": "2007, C Haines, P Galbraith, W Blum, S Khan, Mathematical Modelling: Education, Engineering and Economics - ICTMA 12, Elsevier, page 330",
          "text": "The sequence of Riemann sums is a constant sequence and converges to its constant value s(b) − s(a). No “epsilontics” are needed.",
          "type": "quotation"
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          "ref": "1999, Roland Omnès, Understanding Quantum Mechanics, Princeton University Press, page 185",
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          "ref": "2001, Peter Schuster, Ulrich Berger, Horst Osswald, Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum, Springer Science & Business Media, page 137",
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-04 from the enwiktionary dump dated 2024-05-02 using wiktextract (e9e0a99 and db5a844). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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