# upper bound

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Related to upper bound: Upper Bound and Lower Bound

## upper bound

[¦əp·ər ′bau̇nd] (mathematics)

If

*S*is a subset of an ordered set*A*, an upper bound*b*for*S*in*A*is an element*b*of*A*such that*x*≤*b*for all*x*belonging to*A*.An upper bound on a function ƒ with values in a partially ordered set

*A*is an element of*A*which is larger than every element in the range of ƒ.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## upper bound

An upper bound of two elements x and y under some relation
<= is an element z such that x <= z and y <= z.

("<=" is written in LaTeX as \sqsubseteq).

See also least upper bound.

("<=" is written in LaTeX as \sqsubseteq).

See also least upper bound.

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