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Math Help - Continuous Functions and The intermediate value theorem

  1. #1
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    Continuous Functions and The intermediate value theorem

    Suppose that f is a continuous function on the interval [0,1] and that f(0) = f(1).

    If n is an integer greater than 2, show that:
    f(a) = f(a + (1/n) ) for some a \in [0,1 - (1/n)] .

    How would I approach this question? Would I need to apply mathematics induction?

    Thanks, any help will be highly appreciated.
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    MHF Contributor Calculus26's Avatar
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    Help

    See Latest Posting
    Last edited by Calculus26; May 5th 2009 at 12:30 AM.
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    Hi there, thanks for the reply. I'm still having trouble with the above question.

    Is it correct to do this by induction?
    By showing it is true for n = 3, assume n = k is true and prove n = k + 1 is true.

    But, how would I go about proving n = k + 1 if n = k is true (by induction)?

    Also, is there any other alternative methods of doing this question?

    Thanks
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    MHF Contributor Calculus26's Avatar
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    See the very latest posting
    Last edited by Calculus26; May 5th 2009 at 12:30 AM.
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    MHF Contributor Calculus26's Avatar
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    See the very latest posting
    Last edited by Calculus26; May 5th 2009 at 12:31 AM.
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  6. #6
    MHF Contributor Calculus26's Avatar
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    getting closer

    See the latest following Post ignore this one
    Attached Files Attached Files
    Last edited by Calculus26; May 5th 2009 at 12:32 AM. Reason: want to delete it is a useless post
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  7. #7
    MHF Contributor Calculus26's Avatar
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    Finally--- see the attachment for the proof--with a big debt to Plato
    for showing the direction to go
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