least upper bound

noun, Mathematics

an upper bound that is less than or equal to all the upper bounds of a particular set. 3 is the least upper bound of the set consisting of 1, 2, 3. Abbr.: lub.

Also called supremum.

least upper bound in Technology

theory
(lub or "join", "supremum") The least upper bound of two elements a and b is an upper bound c such that a <= c="" and="" b="" <="c" if="" there="" is="" any="" other="" upper="" bound="" c'="" then="" the="" least="" of="" a="" set="" s="" smallest="" such="" that="" for="" all="" in="" s,="" lub="" mutually="" comparable="" elements="" their="" maximum="" but="" presence="" incomparable="" elements,="" exists,="" it="" will="" be="" some="" element="" greater="" than="" them.="" Lub is the dual to greatest lower bound.
(In LaTeX, "<=" is="" written="" as="" \sqsubseteq, the lub of two elements a and b is written a \sqcup b, and the lub of set S is written as \bigsqcup S).
(1995-02-03)