# least upper bound

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## 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 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).
References in periodicals archive ?
lub], extraterrestrial intelligence is likely to appear only in the presumably few locations where evolution can proceed for longer than the least upper bound of evolution on earth.
The success of utilizing (3) to predict the value of the least upper bound for evolution on earth, given the value of n, is, however, merely apparent because it relies on employing the term [t.
Moreover, the least upper bound on our evolution has a value (albeit unknown to us) that is fixed by factors independent of the evolutionary process.

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