lub ==>
least upper bound
<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)
Nearby terms:
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