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  2. Continuity test - Wikipedia

    en.wikipedia.org/wiki/Continuity_test

    In electronics, a continuity test is the checking of an electric circuit to see if current flows (that it is in fact a complete circuit). A continuity test is performed by placing a small voltage (wired in series with an LED or noise-producing component such as a piezoelectric speaker ) across the chosen path.

  3. Kolmogorov continuity theorem - Wikipedia

    en.wikipedia.org/wiki/Kolmogorov_continuity_theorem

    In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constraints on the moments of its increments will be continuous (or, more precisely, have a "continuous version").

  4. Continuity equation - Wikipedia

    en.wikipedia.org/wiki/Continuity_equation

    A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries.

  5. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy defined continuity of = as follows: an infinitely small increment of the independent variable x always produces an infinitely small change (+) of the dependent variable y (see e.g. Cours d'Analyse, p. 34).

  6. Extreme value theorem - Wikipedia

    en.wikipedia.org/wiki/Extreme_value_theorem

    The basic steps involved in the proof of the extreme value theorem are: Prove the boundedness theorem. Find a sequence so that its image converges to the supremum of . Show that there exists a subsequence that converges to a point in the domain. Use continuity to show that the image of the subsequence converges to the supremum.

  7. Infinitesimal - Wikipedia

    en.wikipedia.org/wiki/Infinitesimal

    [3] Infinitesimals are a basic ingredient in calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. 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 ...

  8. Cantor function - Wikipedia

    en.wikipedia.org/wiki/Cantor_function

    For z = 1/3, the inverse of the function x = 2 C 1/3 (y) is the Cantor function. That is, y = y(x) is the Cantor function. In general, for any z < 1/2, C z (y) looks like the Cantor function turned on its side, with the width of the steps getting wider as z approaches zero.

  9. Lipschitz continuity - Wikipedia

    en.wikipedia.org/wiki/Lipschitz_continuity

    In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem. [2]