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Quick Question about Continuity

  1. Sep 14, 2009 #1
    If f is continuous at x = a, then is it continuous in some neighborhood of x = a as well?
     
  2. jcsd
  3. Sep 14, 2009 #2

    lurflurf

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    No
    A standard example is
    f(x)=x x rational
    f(x)=0 x irrational

    f is continuous at x=0
     
  4. Sep 15, 2009 #3
    And nowhere else. Not even very close to 0.

    --Elucidus
     
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