Complex variables questions, limits and bounds

[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?

 

[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).

 

[futurebird]

Okay. That makes sense.