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Math Help - Extreme Value Theorem

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    Extreme Value Theorem

    Write a proof of the extreme value theorem that is based on the Bolzano-Weierstrass theorem. Thank you!
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    Quote Originally Posted by paulread View Post
    Write a proof of the extreme value theorem that is based on the Bolzano-Weierstrass theorem. Thank you!
    So if this is not a demand, where is your work on this problem?
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    Note: I wrote the question I'm being asked exactly. The "thank you" signifies my appreciation for any help with the proof. How that can be taken as a demand is bewildering to me. Help is no longer needed.
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    Quote Originally Posted by paulread View Post
    Write a proof of the extreme value theorem that is based on the Bolzano-Weierstrass theorem. Thank you!
    Just out of curiosity, how did you do this? I am assuming the full question is something of the sort "If X is a metric space with the B.W.P. and \varphi:X\to\mathbb{R} is continuous that \varphi assumes a max and min on X"?
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    Quote Originally Posted by paulread View Post
    Note: I wrote the question I'm being asked exactly. The "thank you" signifies my appreciation for any help with the proof. How that can be taken as a demand is bewildering to me. Help is no longer needed.
    Quoting myself. Again, I wrote the question EXACTLY. I still don't know any kind of TeX and I'm not sure how you guys get all the math symbols, which is why I haven't shown any of my work. If I need help again I'll be sure to put in as much of an effort in asking the question as I could expect someone to give in answering it for me.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by paulread View Post
    Quoting myself. Again, I wrote the question EXACTLY. I still don't know any kind of TeX and I'm not sure how you guys get all the math symbols, which is why I haven't shown any of my work. If I need help again I'll be sure to put in as much of an effort in asking the question as I could expect someone to give in answering it for me.
    I'm not prompting you to show more work. I am just curious how you solved it. I don't see an easy method right off the bat.
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    See here: Extreme value theorem - Wikipedia, the free encyclopedia
    Exactly using of B.W. theorem to prove that.

    Quote Originally Posted by Drexel28 View Post
    I'm not prompting you to show more work. I am just curious how you solved it. I don't see an easy method right off the bat.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by xxp9 View Post
    See here: Extreme value theorem - Wikipedia, the free encyclopedia
    Exactly using of B.W. theorem to prove that.
    That seems like leaps and bounds to avoid just using the concept of open covers.
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