least upper bound
Synonyms
Examples
Although is also an upper bound, it is not the "least upper bound" and hence is not the "supremum".
By definition, the arc length of a curve is the least upper bound of the lengths of all polygonal approximations of the curve.
Consequently, the supremum is also referred to as the least upper bound (or LUB).
For example, the least upper bound of a bounded increasing computable sequence of computable real numbers need not be a computable real number (Bridges and Richman, 1987:58).
If an ordered set has the property that every nonempty subset of having an upper bound also has a least upper bound, then is said to have the least-upper-bound property.
Minimal upper bounds Finally, a partially ordered set may have many minimal upper bounds without having a least upper bound.