least upper bound


least upper bound

[¦lēst ¦əp·ər ′bau̇nd] (mathematics) The least upper bound of a subset A of a set S with ordering < is="" the="" smallest="" element="" of="">S which is greater than or equal to every element of A. Abbreviated lub. Also known as supremum (sup).

least upper bound

(theory)(lub or "join", "supremum") The least upper bound oftwo elements a and b is an upper bound c such that a <= c andb <= c and if there is any other upper bound c' then c <= c'.The least upper bound of a set S is the smallest b such thatfor all s in S, s <= b. The lub of mutually comparableelements is their maximum but in the presence of incomparableelements, if the lub exists, it will be some other elementgreater than all of them.

Lub is the dual to greatest lower bound.

(In LaTeX, "<=" is written as \\sqsubseteq, the lub of twoelements a and b is written a \\sqcup b, and the lub of set Sis written as \\bigsqcup S).