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Math Help - prove sup and inf

  1. #1
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    Exclamation prove sup and inf

    The question is:

    assume A is a proper subset of B and both belongs to R^n dimention

    show that this implies sup(A)< and= sup(B).

    It looks quite obvious, but I don't know how to construct the proof formally.

    Thanks for help.
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  2. #2
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    Quote Originally Posted by delhaize View Post
    The question is:

    assume A is a proper subset of B and both belongs to R^n dimention

    show that this implies sup(A)< and= sup(B).

    It looks quite obvious, but I don't know how to construct the proof formally.

    Thanks for help.
    Actually, you have a serious problem right from the start. While there is a standard "order" on R, there is no standard order on R^n for n> 1. And without a specific order there is no "lim" or "sup".

    The statement you give is easy to prove in R but makes no sense in R^n for n> 1.
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