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Proving the properties of a real number and a function

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Let E be a subset of the real numbers R, and suppose that E has a least upper bound M which is a real number, i.e. M = sup(E). Let - E be the set - E := { - x : x belongs to E }. Show that - M is the greatest lower bound of - E i.e. - M = inf ( - E)

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This solution shows how to find that a real number is the greatest lower bound of a function.

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