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Math Help - subset, maximum and minimum, supremum and infimum

  1. #1
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    subset, maximum and minimum, supremum and infimum

    about the subset S⊆Q such that x∈S ⇔18x-x^3≧0
    Q is set of rational number.

    a)how to show S have a maximum or not?
    b)how to show S have a minimum or not?
    c)how to show S have supremum or not?
    d) how to show S have infimum or not?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by nyammo View Post
    about the subset S⊆Q such that x∈S ⇔18x-x^3≧0 Q is set of rational number.

    Take into account that

    x\in S\Leftrightarrow 18x-x^3\geq 0\Leftrightarrow\ldots\Leftrightarrow x(3\sqrt{2}-x)(3\sqrt{2}+x)\geq 0

    and \pm 3\sqrt{2}\not\in \mathbb{Q} .
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