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I am a physics undergrad with no experience in analysis and I have not had to do any proofs before. I am taking a class in complex analysis as an elective. I have been doing well in the course so far and improving on my rigour in proofs and such. On to my question:

As epsilon-neighbourhoods were introduced, I understand it completely on an intuitional level, but am having trouble using it in proofs. Does anyone know any good resources with examples to use as I could not find anything.

Thanks for your time!