greatest lower bound
nounUK /ˌɡreɪtɪst ˈləʊə baʊnd/
US /ˌɡreɪtɪst ˈloʊər baʊnd/
The biggest number that is still smaller than or equal to every number in a group.
For the set of numbers greater than 2, the greatest lower bound is 2.
RELATED WORDS
OTHER MEANINGS
2. In a partially ordered set, the greatest element that is less than or equal to every element of a given subset.
In the poset of subsets ordered by inclusion, the greatest lower bound of two sets is their intersection.
3. The infimum of a set, which may or may not belong to the set itself.
The greatest lower bound of the open interval (0, 1) is 0, even though 0 is not in the interval.
4. A value used in real analysis to describe the tightest lower constraint on a collection of numbers.
Every nonempty set of real numbers that is bounded below has a greatest lower bound.