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Math Help - Supremum and Infimum

  1. #1
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    Supremum and Infimum

    I need to find the inf(S) and sup(S)


    I know that they are -1 and 1. I know how to show that both of these are upper bounds. For example in the case of the Supremum, I don't know how to show that v<1 there exists a x>v for some x in S.
    Last edited by hockey777; September 10th 2008 at 10:24 AM.
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  2. #2
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    Quick Thought, would I use density of rationals?
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  3. #3
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    It is true that \left( {\varepsilon  > 0} \right)\left[ {\exists K \mathrel\backepsilon  \quad \frac{1}{K} < \varepsilon } \right]

    Now n = 1 \Rightarrow \quad \frac{1}{1} - \frac{1}{K} > 1 - \varepsilon and m = 1 \Rightarrow \quad \frac{1}{K} - \frac{1}{1} <  - 1 + \varepsilon .
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  4. #4
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    ....
    Last edited by hockey777; September 10th 2008 at 10:24 AM.
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