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High Quality Content by WIKIPEDIA articles! In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (P, ?) is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is lesser than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.