greatest lower bound

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Related to greatest lower bound: Least upper bound, Greatest lower bound property

greatest lower bound

[′grād·əst ¦lō·ər ′bau̇nd]
The greatest lower bound of a set of numbers S is the largest number among the lower bounds of S. Abbreviated glb. Also known as infimum (inf).

greatest lower bound

(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).
References in periodicals archive ?
is the greatest lower bound of the curvature radius G([delta]) outside the spherical strongly charged source.
13] cm is the greatest lower bound of the possible values of the curvature radius of the sphere bounding it.

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