or least upper bound (abbrev. sup, lub), n. the unique smallest member of the set of upper bounds for some given set, equal to its maximum if the given set has a greatest member. The supremum of θ of a set may be defined as satisfying the two conditions θ ≥ t for all t in T, and for all t < θ there is a t' > t in T. For example, the sequence 1/2, 2/3, 3/4,... has as upper bound every real number greater than or equal to 1; it has no maximum, but its supremum is 1. Compare infimum.