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Name of Function

  1. Jan 31, 2004 #1
    The function defined over the real numbers as

    Code (Text):

    f(x) = {0, x rational
           {1, x irrational
     
    appears quite a lot in mathematics textbooks. Does anybody know if this function has a commonly accepted name?
     
  2. jcsd
  3. Jan 31, 2004 #2

    selfAdjoint

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    Well, it's the characteristc function of the set of irrationals, [tex]\chi (R - Q)[/tex].
     
  4. Jan 31, 2004 #3

    Hurkyl

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    I've heard it called the "salt and pepper" function.
     
  5. Jan 31, 2004 #4
  6. Jan 31, 2004 #5
    i've got a simple name and a mnemoic to remember it's name.

    name: the 0 if rational and 1 if irrational function.
    simple mnemoic: tziraoiif
     
  7. Feb 2, 2004 #6
    that doesn't sound simple
     
  8. Feb 3, 2004 #7
    What do you mean? I think it rolls right off the tounge.
     
  9. Feb 3, 2004 #8
    Probably Dirchlet Function(Check Spelling)
     
  10. Feb 3, 2004 #9
    Sure about that? The name Dirichlet has popped quite a number of time in my textbooks. I've never heard of Dirchlet.
     
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