## Quick Reference

*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.

1.0 + eps > 1.0

**From:**
upper bound
in
A Dictionary of Computing »

*Subjects:*
Computing.

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