Hello all,

I have the following problem:

Let be a complex converging sequence.

We want to show that also converges.

I have done the following:

We want to show that converges which means that we have to show that for all there exists such that - We have:

The last inequality comes from the fact that z_{n} converges.

Is the above proof correct? I think that I am assuming that the limit of and are the same??!!

thanks