Floors and ceilings

Question

Suppose that $ n $ is an integer, and $ x $ is a real number, and $ x \ne n $. If $ \lfloor x \rfloor = n $, what are $ \lfloor −x \rfloor $ and $ \lceil −x \rceil $ (express them in terms of $ n $)?

Any thoughts?

Answer 1

To get you started, $ x \ne n $ and $ \lfloor x \rfloor = n $, which means that $ x $ is somewhere between $ n $ and $ n + 1 $. This means that $ -x $ is somewhere between $ -n $ and $ -n - 1 $.