# Floor

The floor function $\mathrm{floor} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written as $\lfloor x \rfloor$) is defined by $$\mathrm{floor}(x) \equiv \lfloor x \rfloor = \max \left\{y \in \mathbb{Z} \colon y \leq x \right\},$$ i.e., it is the largest integer less than or equal to $x$.