What does "supremum" mean?

(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.

What is a synonym for "supremum"?

Common synonyms include: infimum, least upper bound, least upper bound, lub, sup.

How do you pronounce "supremum"?

Pronounced //səˈpɹiːˌmʌm//.

Supremum

//səˈpɹiːˌmʌm// noun

noun ·Rare ·Advanced level

Definitions

Noun

1
(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."