supremum (plural suprema)

  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.
    • 2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, Springer, 3rd Edition, page 8 ↗,
      A sublattice of a lattice is a subset that is closed under pairwise infima and suprema.
    • 2010, James S. Howland, Basic Real Analysis, Jones & Bartlett Learning, page 9 ↗,
      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.
    • 2011, Andreas Löhne, Vector Optimization with Infimum and Supremum, Springer, page vii ↗,
      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.
  • (element of a set greater than or equal to all members of a given subset) least upper bound, LUB, sup

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