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Let X be an ordered set such that every subset S c X has both a supremum and an infimum. Suppose that f : X

Let X be an ordered set such that every subset S c X has both a supremum and an infimum. Suppose that f : X - X is an increasing function, (A) IS (X) J =(5XIX>A 'XA a! Show that there exists an x EX such that f (X) = X

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