supremum

Noun

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Noun

**supremum** (*plural* suprema)

- (
*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**.

- A
**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**.

- The best way to describe the
**2011**, Andreas Löhne,*Vector Optimization with Infimum and*, Springer, page vii ↗,**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.

- The key to an approach to vector optimization based on infimum and

- (
*element of a set greater than or equal to all members of a given subset*) least upper bound, LUB, sup

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002