leastupperboundoflowerbounds
nounUK /liːst ˈʌpə baʊnd ɒv ˈləʊə baʊndz/
US /liːst ˈʌpər baʊnd əv ˈloʊər baʊndz/
The smallest number that is still bigger than or equal to every lower bound in a set.
In the proof, the least upper bound of lower bounds turned out to be the infimum of the set.
OTHER MEANINGS
2. In order theory, the supremum of the set of all lower bounds of a subset.
For the subset of positive rationals, the least upper bound of lower bounds is zero.
3. A lattice-theoretic construction showing when a meet exists in a poset.
The lattice is complete because every subset has a least upper bound of lower bounds.
4. The value that marks the tightest floor shared by all elements of a collection.
Students computed the least upper bound of lower bounds to find the infimum of the interval.