See epsilontics in All languages combined, or Wiktionary
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Algorithms with differentials are already modern.", "type": "quote" }, { "ref": "1981, John M. Ziman, Puzzles, Problems and Enigmas: Occasional Pieces on the Human Aspects of Science, Cambridge University Press, →ISBN, 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.", "type": "quote" }, { "ref": "2009, Detlef Laugwitz, Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Springer Science & Business Media, →ISBN, page 59:", "text": "Both Cauchy and Abel must have been aware that epsilontics is a general tool for making rigorous proofs in analysis, but neither of them, to say nothing of their contemporaries, used it consistently.", "type": "quote" } ], "glosses": [ "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." ], "id": "en-epsilontics-en-noun-lc1GdRua", "links": [ [ "mathematics", "mathematics" ], [ "approach", "approach" ], [ "mathematical analysis", "mathematical analysis" ], [ "explicit", "explicit" ], [ "estimation", "estimation" ], [ "error", "error" ], [ "bound", "bound" ], [ "infinitesimal", "infinitesimal" ] ], "raw_glosses": [ "(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" ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "1973, American Mathematical Society, Notices of the American Mathematical Society:", "text": "Key abstract theorems are explained largely by physical reasoning, and are presented in the most concrete, intelligible fashion possible. Epsilontics are minimized.", "type": "quote" }, { "ref": "1999, Roland Omnès, Understanding Quantum Mechanics, Princeton University Press, →ISBN, 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.", "type": "quote" }, { "ref": "2001, Peter Schuster, Ulrich Berger, Horst Osswald, Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum, Springer Science & Business Media, →ISBN, page 137:", "text": "Thus, Hadamard avoids Weierstrassian epsilontics in his text for engineering students.", "type": "quote" }, { "ref": "2007, C Haines, P Galbraith, W Blum, S Khan, Mathematical Modelling: Education, Engineering and Economics - ICTMA 12, Elsevier, →ISBN, page 330:", "text": "The sequence of Riemann sums is a constant sequence and converges to its constant value s(b) − s(a). 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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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