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!

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- Jul 15th 2011, 09:30 AMvictorluiproblem 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! - Jul 15th 2011, 10:34 AMFernandoRevillaRe: problem with the proof of fundamental theorem of algebra...
As the book says, you only have to apply the definition of continuity, choose $\displaystyle \epsilon=1/2$ .

- Jul 15th 2011, 10:37 AMvictorluiRe: problem with the proof of fundamental theorem of algebra...
May you explain a little more that why i have to chose that number?

- Jul 15th 2011, 10:43 AMFernandoRevillaRe: problem with the proof of fundamental theorem of algebra...
- Jul 15th 2011, 10:46 AMvictorluiRe: problem with the proof of fundamental theorem of algebra...
i think you have to answer that question and post that here because my book never teach me how to use eilson-delta

- Jul 15th 2011, 12:22 PMFernandoRevillaRe: problem with the proof of fundamental theorem of algebra...
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. - Jul 15th 2011, 02:22 PMmr fantasticRe: problem with the proof of fundamental theorem of algebra...
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. - Jul 15th 2011, 02:56 PMPlatoRe: problem with the proof of fundamental theorem of algebra...
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.