Meanings (ES + gloss)
supremo
(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.
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.
Phrases
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