Can an integer "round" to itself? If I asked "When rounding to the tens place, how many different whole numbers will round to 50?" would the answer be "9" or "10". As in: does "50" "round to itself" (in which case, 10) or does it not count because it doesn't "go anywhere" (in which case, 9)?
I can formulate a common-sense rationale for either of these answers. Is there a more "mathematical" answer here?

Wikipedia discusses rounding to integers in terms of the floor and ceiling functions.  Rounding up $x$ is $\lceil x \rceil$, so if $x$ is already an integer, its rounded value doesn't change.
