An example in proving the limit of a complex function says:
Let us show that if in the open disk , then , the point being on the boundary of the domain of definition of .
Observe that when is in the disk , .
Hence, for any such and each positive , whenever .
We simply take .
I understand most parts of the proof. However, I don't know how they got to .
Isn't it that ?
I'm guessing it's because of the domain of definition of , but I don't know how this makes .