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Math Help - Continuous Function

  1. #1
    kamranqau
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    Continuous Function

    Give examples of some functions which are continuous at only one point and discontinuous at all other points of the interval.[B]THANKS
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  2. #2
    Flow Master
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    Quote Originally Posted by kamranqau View Post
    Give examples of some functions which are continuous at only one point and discontinuous at all other points of the interval.[B]THANKS
    The classic example is the function

    f(x) = \left\{ \begin{array}{cl}x, & \mbox{ if } x \mbox{ is rational}\\-x, & \mbox{ if } x \mbox{ is irrational}\end{array}\right.

    It is continuous only at x = 0.
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