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  2. Infinitesimal - Wikipedia

    en.wikipedia.org/wiki/Infinitesimal

    In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective in mathematics, infinitesimal means infinitely small, smaller than any standard real number. Infinitesimals ...

  3. Transcendental law of homogeneity - Wikipedia

    en.wikipedia.org/wiki/Transcendental_law_of...

    Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded. [2] Thus, if a {\displaystyle a} is finite and d x {\displaystyle dx} is infinitesimal, then one sets

  4. Deformation (mathematics) - Wikipedia

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

    Some characteristic phenomena are: the derivation of first-order equations by treating the ε quantities as having negligible squares; the possibility of isolated solutions, in that varying a solution may not be possible, or does not bring anything new; and the question of whether the infinitesimal constraints actually 'integrate', so that ...

  5. Leibniz's notation - Wikipedia

    en.wikipedia.org/wiki/Leibniz's_notation

    The infinitesimal increments are called differentials. Related to this is the integral in which the infinitesimal increments are summed (e.g. to compute lengths, areas and volumes as sums of tiny pieces), for which Leibniz also supplied a closely related notation involving the same differentials, a notation whose efficiency proved decisive in ...

  6. Big O notation - Wikipedia

    en.wikipedia.org/wiki/Big_O_notation

    Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, [1] Edmund Landau, [2] and others, collectively called Bachmann–Landau notation or asymptotic notation.

  7. Hyperreal number - Wikipedia

    en.wikipedia.org/wiki/Hyperreal_number

    The only properties that differ between the reals and the hyperreals are those that rely on quantification over sets, or other higher-level structures such as functions and relations, which are typically constructed out of sets. Each real set, function, and relation has its natural hyperreal extension, satisfying the same first-order properties.

  8. Differential of a function - Wikipedia

    en.wikipedia.org/wiki/Differential_of_a_function

    The differential was first introduced via an intuitive or heuristic definition by Isaac Newton and furthered by Gottfried Leibniz, who thought of the differential dy as an infinitely small (or infinitesimal) change in the value y of the function, corresponding to an infinitely small change dx in the function's argument x.

  9. Rademacher's theorem - Wikipedia

    en.wikipedia.org/wiki/Rademacher's_theorem

    Higher-order concepts such as curvature remain more subtle, since their usual definitions require more differentiability than is achieved by the Rademacher theorem. In the presence of convexity, second-order differentiability is achieved by the Alexandrov theorem, the proof of which can be modeled on that of the Rademacher theorem. In some ...