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Math Help - Question regarding infima and suprema proof

  1. #1
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    Question regarding infima and suprema proof

    I'm trying to answer questions regarding infima and suprema but I am not sure on how to answer this question. It goes like this:

    Let A={ \frac 12, \frac34, \frac 78, \cdots }. Prove that A is unbounded and that sup(A)=1.

    I have rewritten this as:

    A={ 1-\frac 12, 1-\frac14, 1-\frac 18, \cdots }

    So that the n-th term is 1-\frac{1}{2^n}

    I am not sure if I needed to find the n-th term but I am not sure what I can do with this question?

    EDIT I have solved this question now so no need for an answer. Thanks.
    Last edited by MichaelH; December 1st 2013 at 11:16 AM.
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  2. #2
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    Re: Question regarding infima and suprema proof

    Quote Originally Posted by MichaelH View Post
    I'm trying to answer questions regarding infima and suprema but I am not sure on how to answer this question. It goes like this:

    Let A={ \frac 12, \frac34, \frac 78, \cdots }. Prove that A is unbounded and that sup(A)=1.

    I have rewritten this as:

    A={ 1-\frac 12, 1-\frac14, 1-\frac 18, \cdots }

    So that the n-th term is 1-\frac{1}{2^n}

    I am not sure if I needed to find the n-th term but I am not sure what I can do with this question?

    EDIT I have solved this question now so no need for an answer. Thanks.
    do you mean prove it's bounded? an unbounded set or sequence has no supremum.

    From your form of A it's pretty clear A is bounded by 1. Just prove that B=1 is the smallest number that satisfies B > An for all n
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  3. #3
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    Re: Question regarding infima and suprema proof

    To prove that "A is bounded" (as opposed to "bounded above") you need to show also that there is a lower bound. Of course, here, every number is positive so 0 is an obvious lower bound.
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