Definition:Lower Bound of Mapping/Real-Valued

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This page is about lower bounds of real-valued functions which are bounded below. For other uses, see Definition:Lower Bound.

Definition

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


Let $f$ be bounded below in $T$ by $L \in T$.


Then $L$ is a lower bound of $f$.


Lower Bound of Number

When considering the lower bound of a set of numbers, it is commonplace to ignore the set and instead refer just to the number itself.

Thus the construction:

The set of numbers which fulfil the propositional function $P \left({n}\right)$ is bounded below with the lower bound $N$

would be reported as:

The number $n$ such that $P \left({n}\right)$ has the lower bound $N$.


This construct obscures the details of what is actually being stated. Its use on $\mathsf{Pr} \infty \mathsf{fWiki}$ is considered an abuse of notation and so discouraged.


This also applies in the case where it is the lower bound of a mapping which is under discussion.


Also see


Sources