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Alexmahone
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- Jan 26, 2012
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Let $S$ be a non-empty bounded set of real numbers, and $\overline{m}=\sup S$. Prove that $\inf \{\overline{m}-x: x\in S\}=0$.
[Use only the definitions of supremum and infimum, and not identities like $\inf(A+B)=\inf A+\inf B$ and $\inf(-S)=-\sup(S)$.]
[Use only the definitions of supremum and infimum, and not identities like $\inf(A+B)=\inf A+\inf B$ and $\inf(-S)=-\sup(S)$.]
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