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upper bound

upper bound
1. of a set S on which the partial ordering < is defined. An element u with the property that s < u for all s in S. Also u is a least upper bound if, for any other upper bound v, u < v.

Since numerical computing demands the truncation of infinite arithmetic to finite arithmetic, the computation of least upper 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 lower bound.

2. of a matrix or vector. See array.

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