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  1. Limit (mathematics) - Wikipedia

    • In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. 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 t… See more

    History

    According to Hankel (1871), the modern concept of limit originates from Proposition X.1 of Euclid's Elements, which … See more

    Types of limits

    The expression 0.999... should be interpreted as the limit of the sequence 0.9, 0.99, 0.999, ... and so on. This sequence can be rigorously shown to have the limit 1, and therefore this expression is meaningfull… See more

    Uses

    Limits are used to define a number of important concepts in analysis.
    A particular expression of interest which is formalized as the limit of a sequence is sums of infinite series. These are "infinite sums" of re… See more

    Properties

    For sequences of real numbers, a number of properties can be proven. Suppose and are two sequences converging to and respectively.
    • Sum of limits is equal to limit of sum
    • Product … See more

    See also

    Asymptotic analysis: a method of describing limiting behavior
    Banach limit defined on the Banach space that extends the usual limits.
    Convergence of random variablesSee more

     
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