Definition
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[08T] Let \(A β β\) be not be empty. Recall that the supremum, or least upper bound, of a set \(A\) is the minimum of majorants; We will indicate it with the usual writing \(\sup A\). If \(A\) is bounded above then \(\sup A\) is a real number; otherwise, by convention, it is set to \(\sup A=+β\).