In
mathematics, given a subset S of a
partially ordered set T, the supremum of S, if it exists, is the
least element of T that is greater than or equal to each element of S. Consequently, the supremum is also referred to as the least upper bound, lub or LUB. If the supremum exists, it may or may not belong to S. If the supremum exists, it is unique. Suprema are often considered for subsets of
real numbers,
rational numbers, or any other well-known mathematical structure for which it is immediately clear what it means for an element to be "greater-than-or-equal-to" another element. The definition generalizes easily to the more abstract setting of
order theory, where one considers arbitrary
partially ordered sets.
See more at Wikipedia.org...
<
theory> (lub or "join", "supremum") The least upper bound of two elements a and b is an upper bound c such that a greatest lower bound.
(In
LaTeX, "\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)
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