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Complex variables questions, limits and bounds

  1. Dec 15, 2007 #1
    If I have a function f(z) such that limit z --> infinity is finite what do I know about that function?

    Is it "bounded" or am I still confused about what "bounded" means?
  2. jcsd
  3. Dec 15, 2007 #2

    Ben Niehoff

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    Bounded means that |f(z)| stays less than some finite value B for ALL z. So, no. For example,

    [tex]\lim_{z->\infty} \frac{1}{z} = 0[/tex]

    but f(z)=1/z is not bounded (it blows up at z=0).
  4. Dec 15, 2007 #3
    Okay. That makes sense.
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