For a real number \(x,\) find the number of different possible values of \(\lfloor x \rfloor + \lfloor -x \rfloor.\)
\(x \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = 0\\ x \not \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = -1\)
