lower bound

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1 of a set S on which the partial ordering < is defined. An element l with the property that l < s for all s in S. Also l is a greatest lower bound if, for any other lower bound h, h < l.

Since numerical computing demands the truncation of infinite arithmetic to finite arithmetic, the computation of greatest lower bounds of real numbers, indeed of any limit, can only be achieved to a machine tolerance, usually defined to be machine precision: the smallest epsilon eps, such that

1.0 + eps > 1.0

in computer arithmetic. See also upper bound.

2 of a matrix or vector. See array.

Subjects: Computing.

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