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).

(1995-02-03)