# Definition:Upper Bound of Number

## Definition

When considering the upper 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 above with the upper bound $N$

would be reported as:

The number $n$ such that $P \left({n}\right)$ has the upper 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 upper bound of a mapping which is under discussion.