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 $\map P n$ is bounded above with the upper bound $N$

would be reported as:


 * The number $n$ such that $\map P n$ has the upper bound $N$.

This construct obscures the details of what is actually being stated. Its use on 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.