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Math Help - coefficient of supremum proof

  1. #1
    MHF Contributor
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    coefficient of supremum proof

    S is a bounded non empty group.i need to prove that sup(cS)=csupS
    if c=0 then it trivial
    if c>0 then we need to prove that the smallest upper bound to cS is
    csupS
    this is how the book proves:
    we take s\in S s<csupS \frac{s}{c}<supS so \frac{s}{c} cannot
    be the supremum and there is x\in S for which x>\frac{s}{c}.
    i cant understand why it proves the law??
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  2. #2
    MHF Contributor

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    Re: coefficient of supremum proof

    It doesn't. I recommend you go back and re-read your book. You are saying that you want to prove that c sup(S) is equal to sup(cS) and, if it were correct, what you write would prove it is NOT.
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