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  2. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    This is a list of limits for common functions such as elementary functions. In this article, the terms a, b and c are constants with respect to x.

  3. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    The limit inferior of a sequence (xn) is defined by or Similarly, the limit superior of (xn) is defined by or Alternatively, the notations and are sometimes used. The limits superior and inferior can equivalently be defined using the concept of subsequential limits of the sequence . [1] An element of the extended real numbers is a subsequential limit of if there exists a strictly increasing ...

  4. Limit (category theory) - Wikipedia

    en.wikipedia.org/wiki/Limit_(category_theory)

    In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits. Limits and colimits, like the strongly related notions of universal properties ...

  5. Limit (mathematics) - Wikipedia

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

    In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely ...

  6. Interchange of limiting operations - Wikipedia

    en.wikipedia.org/wiki/Interchange_of_limiting...

    In mathematics, the study of interchange of limiting operations is one of the major concerns of mathematical analysis, in that two given limiting operations, say L and M, cannot be assumed to give the same result when applied in either order. One of the historical sources for this theory is the study of trigonometric series. [1]

  7. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which may or may not be in the domain of the function. Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f(x) to every input x. We say that the function has a limit L at ...

  8. Computation in the limit - Wikipedia

    en.wikipedia.org/wiki/Computation_in_the_limit

    Limit of a uniformly computable sequence of functionsIn computability theory, a function is called limit computable if it is the limit of a uniformly computable sequence of functions. The terms computable in the limit, limit recursive and recursively approximable are also used. One can think of limit computable functions as those admitting an eventually correct computable guessing procedure at ...

  9. The Legend of Mai An Tiêm - Wikipedia

    en.wikipedia.org/wiki/The_Legend_of_Mai_An_Tiêm

    Watermelons are an iconic fruit in Vietnamese New Year The Legend of Mai An Tiêm (Vietnamese: Truyền thuyết Mai An Tiêm) or the Origin Tale of Watermelons (Vietnamese: Sự tích quả dưa hấu) is a Vietnamese folktale and myth, first told in Lĩnh Nam chích quái. It narrates the life of Mai An Tiêm, a culture hero living in the Hùng king 's era and his discovery of watermelons ...