supremum
nounUK /səˈpɹiːˌmʌm/ · CA, US /səˈpɹiˌmʌm/
Etymology Borrowed from Latin supremum.
1
Mathematics, Sciences, 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:
1 more example
- 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:
- Derived terms
- essential supremum
- Related terms
- maximum