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Function Question

  1. Sep 20, 2007 #1
    Let f be the function that takes the value of 1 on all rational numbers, and 0 on all irrational numbers. At what points is f continuous?

    Does anyone know how to do this?? I mean, there are just so many points to point out...such as square root of 2 and 10, and the list is endless...
  2. jcsd
  3. Sep 20, 2007 #2
    I'm fairly sure it's not continuous anywhere. Specifically, for any neighbourhood about any point, will contain some rationals and some irrationals, and so a sequence of decreasing neighbourhoods don't converge to any value.
  4. Sep 20, 2007 #3
    I see! Thanks a lot!
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