supremum

Etymology

Borrowed from Latin supremum.

noun

1. (set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.
   A sublattice of a lattice is a subset that is closed under pairwise infima and suprema. 2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edition, Springer, page 8
   The best way to describe the supremum of S is to say that it wants to be the greatest element of S. In fact, if S has a greatest element, then that element is the supremum. 2010, James S. Howland, Basic Real Analysis, Jones & Bartlett Publishers, page 9
   The key to an approach to vector optimization based on infimum and supremum is to consider set-based objective functions and to extend the partial ordering of the original objective space to a suitable subspace of the power set. In this new space the infimum and supremum exist under the usual assumptions. 2011, Andreas Löhne, Vector Optimization with Infimum and Supremum, Springer, page vii