or greatest lower bound (abbrev. inf, glb), n. the unique largest member of the set of lower bounds for some given set, equal to its minimum if the given set has a least member. The infimum θ of a set T may be defined as satisfying the two conditions, that θ ≤ t for all t in T, and that for all t > θ there is a t' < t in T. For example, the geometric sequence 1/2, 1/4, 1/8,... has as a lower bound every real number less than or equal to zero; it has no least member, and so no minimum but its infimum is 0. Compare supremum.