# 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] (mathematics)

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).McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## greatest lower bound

(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).

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).

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