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    Removable Discontinuity

    Definition

    Let f(x) be a real-valued function and let a be a number in the domain of f(x). If lim_(x->a) f(x) = L!=f(a), where L is a real number, then f(x) has a removable discontinuity at a. A removable discontinuity can be "fixed" by defining a new function g(x) so that lim_(x->a) g(x) = L = g(a). That is, the new function g(x) = piecewise f(x) L for x!=a for x = a is continuous at a.

    Details

    function | limit of a function

    jump discontinuity | infinite discontinuity | discontinuous function | continuous function

    Associated person

    Bernard Placidus Johann Nepomuk Bolzano

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