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Math Help - Supreme of a set

  1. #1
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    Supreme of a set

    I know it is not necessary for the supreme of a set be an element of the set.
    Can someone please justify this by giving suitable examples?
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  2. #2
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    Re: Supreme of a set

    Quote Originally Posted by Kristen111111111111111111 View Post
    I know it is not necessary for the supreme of a set be an element of the set.
    Can someone please justify this by giving suitable examples?
    Suppose that S = \left\{ {1 - {n^{ - 1}}:n \in {Z^ + }} \right\}.

    Now surely \sup(S)=1. BUT tell us if 1\in S~?
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  3. #3
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    Re: Supreme of a set

    Yeah that's superb! Thanks a lot
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  4. #4
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    Re: Supreme of a set

    Similarly: the set of all real number less than one. 1 is the supremum but 1 is not in the set.
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