Let $u: \mathbb{R} \rightarrow \mathbb{R}$, $u(x)=\lfloor x\rfloor$.
(i) Determine $\{u \geq a\}$ for all $a \in \mathbb{R}$.
(ii) Show that $u$ is $\mathcal{B}(\mathbb{R}) / \mathcal{B}(\mathbb{R})$-measureable.
(i) I'm not sure what the notation mean. I guess it is $\{u: u \ge a,\forall a\in\mathbb{R}\}$. But this will just be all the integers by the definition of $u$. (?)
(ii) I can probably do this one myself.