Definition:Upper Bound of Mapping

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This page is about upper bounds of mappings which are bounded above. For other uses, see Definition:Upper Bound.

Definition

Let $f: S \to T$ be a mapping whose codomain is an ordered set $\left({T, \preceq}\right)$.


Let $f$ be bounded above in $T$ by $H \in T$.


Then $H$ is an upper bound of $f$.


Real-Valued Function

The concept is usually encountered where $\left({T, \preceq}\right)$ is the set of real numbers under the usual ordering $\left({\R, \le}\right)$:


Let $f: S \to \R$ be a real-valued function.


Let $f$ be bounded above in $\R$ by $H \in \R$.


Then $H$ is an upper bound of $f$.


Also see