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  2. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    As an example, the function H(t) denoting the height of a growing flower at time t would be considered continuous. In contrast, the function M ( t ) denoting the amount of money in a bank account at time t would be considered discontinuous since it "jumps" at each point in time when money is deposited or withdrawn.

  3. Continuous or discrete variable - Wikipedia

    en.wikipedia.org/wiki/Continuous_or_discrete...

    For example, a variable over a non-empty range of the real numbers is continuous, if it can take on any value in that range. [4] Methods of calculus are often used in problems in which the variables are continuous, for example in continuous optimization problems. [5]

  4. List of continuity-related mathematical topics - Wikipedia

    en.wikipedia.org/wiki/List_of_continuity-related...

    Continuous probability distribution: Sometimes this term is used to mean a probability distribution whose cumulative distribution function (c.d.f.) is (simply) continuous. Sometimes it has a less inclusive meaning: a distribution whose c.d.f. is absolutely continuous with respect to Lebesgue measure. This less inclusive sense is equivalent to ...

  5. Uniform continuity - Wikipedia

    en.wikipedia.org/wiki/Uniform_continuity

    The converse does not hold, since the function :, is, as seen above, not uniformly continuous, but it is continuous and thus Cauchy continuous. In general, for functions defined on unbounded spaces like R {\displaystyle R} , uniform continuity is a rather strong condition.

  6. Lipschitz continuity - Wikipedia

    en.wikipedia.org/wiki/Lipschitz_continuity

    A function is called locally Lipschitz continuous if for every x in X there exists a neighborhood U of x such that f restricted to U is Lipschitz continuous. Equivalently, if X is a locally compact metric space, then f is locally Lipschitz if and only if it is Lipschitz continuous on every compact subset of X. In spaces that are not locally ...

  7. Closed graph theorem - Wikipedia

    en.wikipedia.org/wiki/Closed_graph_theorem

    So, if the open mapping theorem holds for ; i.e., is an open mapping, then is continuous and then is continuous (as the composition of continuous maps). For example, the above argument applies if is a linear operator between Banach spaces with closed graph, or if is a map with closed graph between compact Hausdorff spaces.

  8. Weierstrass function - Wikipedia

    en.wikipedia.org/wiki/Weierstrass_function

    It is also an example of a fractal curve. The Weierstrass function has been historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. [1]

  9. Discrete time and continuous time - Wikipedia

    en.wikipedia.org/wiki/Discrete_time_and...

    A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum (e.g., a connected interval of the reals). That is, the function's domain is an uncountable set. The function itself need not to be continuous.