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Math Help - Real Analysis Prove continuous

  1. #1
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    Real Analysis Prove continuous

    f: [0,1]--> R (reals)

    f(x) = {1 if x= 1/n where nEN (element Naturals) , 0 otherwise}

    Prove f is continuous at 1/pi

    Thank for the help on the previous problem, I have not been able to make any progress on this problem and need help please.
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  2. #2
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    Re: Real Analysis Prove continuous

    Show that there is some delta neighbourhood around 1/pi which does not contain a number of the form 1/n, with n a natural number. Then the function evaluated at each point of this neighbourhood is identically zero, which is the value of f(1/pi). A quick epsilon-delta proof finishes this problem off.
    Thanks from topsquark and leonhart
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