Homework Help: Complex variables questions, limits and bounds

1. Dec 15, 2007

futurebird

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. Dec 15, 2007

Ben Niehoff

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

$$\lim_{z->\infty} \frac{1}{z} = 0$$

but f(z)=1/z is not bounded (it blows up at z=0).

3. Dec 15, 2007

futurebird

Okay. That makes sense.

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