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).

greatest lower bound

(theory)(glb, meet, infimum) The greatest lower bound of twoelements, a and b is an element c such that c <= a and c <= band if there is any other lower bound c' then c' <= c.

The greatest lower bound of a set S is the greatest element bsuch that for all s in S, b <= s. The glb of mutuallycomparable elements is their minimum but in the presence ofincomparable elements, if the glb exists, it will be someother element less than all of them.

glb is the dual to least upper bound.

(In LaTeX "<=" is written as \\sqsubseteq, the glb of twoelements a and b is written as a \\sqcap b and the glb of setS as \\bigsqcap S).

单词	greatest lower bound
释义	DictionarySeeinfimum greatest lower bound 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). greatest lower bound (theory)(glb, meet, infimum) The greatest lower bound of twoelements, a and b is an element c such that c <= a and c <= band if there is any other lower bound c' then c' <= c. The greatest lower bound of a set S is the greatest element bsuch that for all s in S, b <= s. The glb of mutuallycomparable elements is their minimum but in the presence ofincomparable elements, if the glb exists, it will be someother element less than all of them. glb is the dual to least upper bound. (In LaTeX "<=" is written as \\sqsubseteq, the glb of twoelements a and b is written as a \\sqcap b and the glb of setS as \\bigsqcap S). AcronymsSeeGLB
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