Meaning of Supremum | Babel Free

Definitions

(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.

Equivalents

Examples

“A sublattice of a lattice is a subset that is closed under pairwise infima and suprema.”

“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.”

“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.”

CEFR level