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Math Help - problem with the proof of fundamental theorem of algebra...

  1. #1
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    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!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    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 .
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  3. #3
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    Re: problem with the proof of fundamental theorem of algebra...

    May you explain a little more that why i have to chose that number?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: problem with the proof of fundamental theorem of algebra...

    Quote Originally Posted by victorlui View Post
    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?
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  5. #5
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    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
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Re: problem with the proof of fundamental theorem of algebra...

    Quote Originally Posted by victorlui View Post
    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.
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  7. #7
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    Re: problem with the proof of fundamental theorem of algebra...

    Quote Originally Posted by victorlui View Post
    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.
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  8. #8
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    Re: 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 Rossís Elementary Analysis.
    An author such as Shilov is a challenge for even advanced students.
    Elliott Mendelsonís Number Systems and the Foundations of Analysis in the Dover edition is quite inexpensive.
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