subset, maximum and minimum, supremum and infimum

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March 22nd 2011, 08:00 AM
nyammo

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?
March 22nd 2011, 09:43 AM
FernandoRevilla

Quote:

Originally Posted by nyammo

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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