# problem with the proof of fundamental theorem of algebra...

• Jul 15th 2011, 10:30 AM
victorlui
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!
• Jul 15th 2011, 11:34 AM
FernandoRevilla
Re: problem with the proof of fundamental theorem of algebra...
As the book says, you only have to apply the definition of continuity, choose $\epsilon=1/2$ .
• Jul 15th 2011, 11:37 AM
victorlui
Re: 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, 11:43 AM
FernandoRevilla
Re: problem with the proof of fundamental theorem of algebra...
Quote:

Originally Posted by victorlui
May you explain a little more that why i have to chose that number?

What does mean $f:\mathbb{C}\to \mathbb{C}$ continuous at $0$ and $f(0)=0$ ?. Please write the definition and after that choose $\epsilon=1/2$. What do you obtain?
• Jul 15th 2011, 11:46 AM
victorlui
Re: 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, 01:22 PM
FernandoRevilla
Re: problem with the proof of fundamental theorem of algebra...
Quote:

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.
• Jul 15th 2011, 03:22 PM
mr fantastic
Re: problem with the proof of fundamental theorem of algebra...
Quote:

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.
• Jul 15th 2011, 03:56 PM
Plato
Re: problem with the proof of fundamental theorem of algebra...
I will second and underline what Mr. F posted above.