Supremum | Surface Runoff, Mathematics, Partially Ordered Set, Greatest Element, Real Number, Rational Number, Maximal Element, Upper and Lower Bounds, Mathematical Analysis. Questo articolo non è disponibile.Supremum | Surface Runoff, Mathematics, Partially Ordered Set, Greatest Element, Real Number, Rational Number, Maximal Element, Upper and Lower Bounds, Mathematical Analysis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, given a subset S of a partially ordered set T, the supremum (sup) of S, if it exists, is the least element of T that is greater than or equal to each element of S. Consequently, the supremum is also referred to as the least upper bound, lub or LUB. If the supremum exists, it may or may not belong to S. If the supremum exists, it is unique. Suprema are often considered for subsets of real numbers, rational numbers, or any other well-known mathematical structure for which it is immediately clear what it means for an element to be greater-than-or-equal-to" another element. The definition generalizes easily to the more abstract setting of order theory, where one considers arbitrary partially ordered sets."