# greatest lower bound

## greatest lower bound

noun
a lower bound that is greater than or equal to all the lower bounds of a given set: 1 is the greatest lower bound of the set consisting of 1, 2, 3. Abbreviation: glb
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### greatest lower bound definition

theory
(glb, meet, infimum) The greatest lower bound of two elements, a and b is an element c such that c <= a and c <= b and if there is any other lower bound c' then c' <= c.
The greatest lower bound of a set S is the greatest element b such that for all s in S, b <= s. The glb of mutually comparable elements is their minimum but in the presence of incomparable elements, if the glb exists, it will be some other element less than all of them.
glb is the dual to least upper bound.
(In LaTeX "<=" is written as \sqsubseteq, the glb of two elements a and b is written as a \sqcap b and the glb of set S as \bigsqcap S).
(1995-02-03)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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