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  2. Template:Infinitesimals - Wikipedia

    en.wikipedia.org/wiki/Template:Infinitesimals

    A navigational box that can be placed at the bottom of articles. Template parameters [Edit template data] Parameter Description Type Status State state The initial visibility of the navbox Suggested values collapsed expanded autocollapse String suggested Template transclusions Transclusion maintenance Check completeness of transclusions The above documentation is transcluded from Template ...

  3. Infinitesimal - Wikipedia

    en.wikipedia.org/wiki/Infinitesimal

    Infinitesimals (ε) and infinities (ω) on the hyperreal number line (ε = 1/ω) In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-eth" item in a sequence.

  4. Elementary Calculus: An Infinitesimal Approach - Wikipedia

    en.wikipedia.org/wiki/Elementary_Calculus:_An...

    [1] [6] Despite the benefits described by Sullivan, the vast majority of mathematicians have not adopted infinitesimal methods in their teaching. [7] Recently, Katz & Katz [8] give a positive account of a calculus course based on Keisler's book. O'Donovan also described his experience teaching calculus using infinitesimals.

  5. Nonstandard calculus - Wikipedia

    en.wikipedia.org/wiki/Nonstandard_calculus

    Keisler's Elementary Calculus: An Infinitesimal Approach defines continuity on page 125 in terms of infinitesimals, to the exclusion of epsilon, delta methods. The derivative is defined on page 45 using infinitesimals rather than an epsilon-delta approach. The integral is defined on page 183 in terms of infinitesimals.

  6. Smooth infinitesimal analysis - Wikipedia

    en.wikipedia.org/wiki/Smooth_infinitesimal_analysis

    This approach departs from the classical logic used in conventional mathematics by denying the law of the excluded middle, e.g., NOT (a ≠ b) does not imply a = b.In particular, in a theory of smooth infinitesimal analysis one can prove for all infinitesimals ε, NOT (ε ≠ 0); yet it is provably false that all infinitesimals are equal to zero. [2]

  7. Leibniz's notation - Wikipedia

    en.wikipedia.org/wiki/Leibniz's_notation

    Robinson's methods are used by only a minority of mathematicians. Jerome Keisler wrote a first-year calculus textbook, Elementary calculus: an infinitesimal approach , based on Robinson's approach. From the point of view of modern infinitesimal theory, Δ x is an infinitesimal x -increment, Δ y is the corresponding y -increment, and the ...

  8. Differential (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Differential_(mathematics)

    In traditional approaches to calculus, differentials (e.g. dx, dy, dt, etc.) are interpreted as infinitesimals. There are several methods of defining infinitesimals rigorously, but it is sufficient to say that an infinitesimal number is smaller in absolute value than any positive real number, just as an infinitely large number is larger than ...

  9. Hyperreal number - Wikipedia

    en.wikipedia.org/wiki/Hyperreal_number

    Recall that the sequences converging to zero are sometimes called infinitely small. These are almost the infinitesimals in a sense; the true infinitesimals include certain classes of sequences that contain a sequence converging to zero. Let us see where these classes come from. Consider first the sequences of real numbers.