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Continuous functions

  1. Nov 11, 2008 #1
    Is there a function f:R-->R that is continuous at π and discontinuous at all other numbers?


    1. The problem statement, all variables and given/known data

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    3. The attempt at a solution
  2. jcsd
  3. Nov 11, 2008 #2


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    Consider the function f(x)=0 for x irrational and f(x)=x for x rational. Where is that continuous? Can you modify that for your purposes?
  4. Nov 12, 2008 #3
    So f(x)=(x-π)^18 for x rational and 0 otherwise should work I think!

    Thank you very much
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