Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?

    Thx

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



    2. Relevant equations



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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook