Thread: problem with the proof of fundamental theorem of algebra...

please see here(p.174-175 Elementary real and complex analysis
By Georgiĭ Evgenʹevich Shilov):
Elementary real and complex analysis - Google Books

problem is:
How does modulus (H(z))<1/2
in p.175?
it doesn't make sense to me!

As the book says, you only have to apply the definition of continuity, choose .

May you explain a little more that why i have to chose that number?

Originally Posted by victorlui

May you explain a little more that why i have to chose that number?

What does mean continuous at and ?. Please write the definition and after that choose . What do you obtain?

i think you have to answer that question and post that here because my book never teach me how to use eilson-delta

Originally Posted by victorlui

i think you have to answer that question and post that here because my book never teach me how to use eilson-delta

I think you have to answer to my question. If you are not able, better forget the book. You are trying impossible things.

P.S. There is a lot of people in this forum who honestly try to help. So, I consider a lack of courtesy on your part to decide the way we have to answer.

Originally Posted by victorlui

i think you have to answer that question and post that here because my book never teach me how to use eilson-delta

I have said repeatedly that you lack the pre-requisite knowledge to understand most of the answers to the questions you're asking.

It is not our job to teach you. Before you try to run, learn to walk. Before you try to walk, learn to crawl. Otherwise, a lot of people, including you, are going to get very frustrated.

I will second and underline what Mr. F posted above.
I will add a suggestion. Forget Google Books.
Get yourself an actual textbook suitable for you lack of background in these matters. I suggest that you look at an elementary text such as Ken Ross’s Elementary Analysis.
An author such as Shilov is a challenge for even advanced students.
Elliott Mendelson’s Number Systems and the Foundations of Analysis in the Dover edition is quite inexpensive.