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.

Also called infimum.

greatest lower bound in Technology

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" if="" there="" is="" any="" other="" lower="" bound="" c'="" then="" 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="" presence="" incomparable="" elements,="" if="" exists,="" it="" will="" be="" some="" other="" element="" less="" than="" all="" 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)