least upper bound

1 definition found

least upper bound - Free On-line Dictionary of Computing (26 May 2007) :

  least upper bound
  lub
  supremum
  
     <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 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)