Source : Free On-Line Dictionary of Computing

least upper bound
     
         (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 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 that
        for all s in S, s <= b.  The lub of mutually comparable
        elements is their maximum but in the presence of incomparable
        elements, if the lub exists, it will be some other element
        greater than all of 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)