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What does a function takes on mean?

  1. Nov 8, 2013 #1
    What does "a function takes on" mean?

    Hey! I'm currently learning Picard's theorem, but I don't quite understand it because of difficult words..

    In the text, it uses the term "takes on", ie

    "If f(z) is analytic and has an isolated essential singularity at a point z_0, it takes on every value, with at most one exceptional value in an arbitrarily small ε-neighbourhood of z_0".

    What does "take on" mean? Are they talking about the function's range? And what do they mean with "exceptional value"?
     
  2. jcsd
  3. Nov 8, 2013 #2

    Stephen Tashi

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    Science Advisor

    Yes - or technically the "image" of the function. http://en.wikipedia.org/wiki/Codomain

    It means a complex number c such that y=c is an exception to the statement "the function's image contains the value y". That is, y = c makes the statement false.
     
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