Kenneth Rosen Edition 7 Exercise 2.3 Question 48 (Page No. 154)

Question

Show that if $x$ is a real number, then $\left \lceil x \right \rceil - \left \lfloor x \right \rfloor =1$ if $x$ is not an integer and $\left \lceil x \right \rceil - \left \lfloor x \right \rfloor =0$ if $x$ is an integer.