4. Let $[x]$ denote the greatest integer not exceeding $x$, and $\mathbf{Z}$ denote the set of integers. The solution set of the equation $[x]^{3}-[x]^{2}=x^{3}-x^{2}$ is $M$. Then, $(\quad)$.
(A) $M \subset \mathbf{Z}$
(B) $\mathbf{Z} \subset M$
(C) $M=\mathbf{Z}$
(D) $M$ and $\mathbf{Z}$ are not subsets of each other
4.C.

Obviously, $\mathbf{Z} \subset M$.
Let $x \in M$, and let $x=t+\alpha$ (where $t \in \mathbf{Z}, 0 \leqslant \alpha < 1$).
Then $3 t^{2}+(3 \alpha-2) t+\alpha^{2}-\alpha>0$.
Thus, $\alpha=0$.
When $t=0$, $\alpha^{2}-\alpha=0$, so $\alpha=0$, which means $x \in \mathbf{Z}$, hence $M \subset \mathbf{Z}$.
Therefore, $M=\mathbf{Z}$.