greatest common divisor

<mathematics>

(GCD) A function that returns the largest positive integer that both arguments are integer multiples of.

See also Euclid's Algorithm. Compare: lowest common multiple.

Last updated: 1999-11-02

greatest lower bound

<theory>

(glb, meet, infimum) The greatest lower bound of two elements, a and b is an element c such that c <= a and c <= b and if there is any other lower bound c' then c' <= c.

The greatest lower bound of a set S is the greatest element b such that for all s in S, b <= s. The glb of mutually comparable elements is their minimum but in the presence of incomparable elements, if the glb exists, it will be some other element less than all of them.

glb is the dual to least upper bound.

(In LaTeX "<=" is written as \sqsubseteq, the glb of two elements a and b is written as a \sqcap b and the glb of set S as \bigsqcap S).

Last updated: 1995-02-03

Nearby terms:

greater than ♦ greatest common divisor ♦ greatest lower bound ♦ Great Renaming

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