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  2. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    e. 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.

  3. Limit inferior and limit superior - Wikipedia

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

    Limit inferior and limit superior. In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points ...

  4. Limit (mathematics) - Wikipedia

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

    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 ...

  5. Central limit theorem - Wikipedia

    en.wikipedia.org/wiki/Central_limit_theorem

    The scaled sum of a sequence of i.i.d. random variables with finite positive variance converges in distribution to the normal distribution. In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution.

  6. Kuratowski convergence - Wikipedia

    en.wikipedia.org/wiki/Kuratowski_convergence

    Kuratowski convergence. In mathematics, Kuratowski convergence or Painlevé-Kuratowski convergence is a notion of convergence for subsets of a topological space. First introduced by Paul Painlevé in lectures on mathematical analysis in 1902, [1] the concept was popularized in texts by Felix Hausdorff [2] and Kazimierz Kuratowski. [3 ...

  7. Direct limit - Wikipedia

    en.wikipedia.org/wiki/Direct_limit

    Basic concepts. Commutative algebra. Noncommutative algebra. v. t. e. In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector spaces or in general objects from any category.

  8. Banach limit - Wikipedia

    en.wikipedia.org/wiki/Banach_limit

    Banach limit. In mathematical analysis, a Banach limit is a continuous linear functional. {\displaystyle \phi :\ell ^ {\infty }\to \mathbb {C} } defined on the Banach space of all bounded complex -valued sequences such that for all sequences , in , and complex numbers : {\displaystyle \phi (\alpha x+y)=\alpha \phi (x)+\phi (y)}

  9. One-sided limit - Wikipedia

    en.wikipedia.org/wiki/One-sided_limit

    One-sided limit. In calculus, a one-sided limit refers to either one of the two limits of a function of a real variable as approaches a specified point either from the left or from the right. [1][2] The limit as decreases in value approaching ( approaches "from the right" [3] or "from above") can be denoted: [1][2] The limit as increases in ...