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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 . Limits for general functions

  3. List of continuity-related mathematical topics - Wikipedia

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

    Continuous function; Absolutely continuous function; Absolute continuity of a measure with respect to another measure; Continuous probability distribution: Sometimes this term is used to mean a probability distribution whose cumulative distribution function (c.d.f.) is (simply) continuous.

  4. 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 .

  5. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    In particular, one can no longer talk about the limit of a function at a point, but rather a limit or the set of limits at a point. A function is continuous at a limit point p of and in its domain if and only if f(p) is the (or, in the general case, a) limit of f(x) as x tends to p. There is another type of limit of a function, namely the ...

  6. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    This notion of continuity is the same as topological continuity when the partially ordered sets are given the Scott topology. [ 19 ] [ 20 ] In category theory , a functor F : C → D {\displaystyle F:{\mathcal {C}}\to {\mathcal {D}}} between two categories is called continuous if it commutes with small limits .

  7. Interchange of limiting operations - Wikipedia

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

    Examples abound, one of the simplest being that for a double sequence a m,n: it is not necessarily the case that the operations of taking the limits as m → ∞ and as n → ∞ can be freely interchanged. [4] For example take a m,n = 2 m − n. in which taking the limit first with respect to n gives 0, and with respect to m gives ∞.

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