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If A is nonempty and has an upper bound proof that inf(-A)=-sup(A). And if A has a lower bound sup(-A)=-inf(A). I've already shown that -A has lower bound for first case and has an upper bound for second.

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marked as duplicate by Daniel Fischer, Hakim, Namaste, Claude Leibovici, Davide Giraudo Oct 18 '14 at 12:17

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