What Is the Domain of the Greatest Integer Function, Given $f(x)=[[x]]$

Multiple Choice

What is the domain of the greatest integer function, given by $f(x) =[[x]]$ ?

A) $\{\ldots,-2,-1,0,1,2, \ldots\}$
B) $[0, \infty)$
C) $(-\infty, \infty)$
D) $\{0,1,2, \ldots\}$