# Floor and Ceiling Function > [!Example] Floor Function > The *floor [[function]]* is a function with [[domain]] $\mathbb{R}$ and [[image]] $\mathbb{Z}$ defined as > $\lfloor x\rfloor = \max\{m\in\mathbb{Z}\mid m\le x\}$ > Its output is the *largest integer less than or equal to* $x$. > > ![[FloorFunction.svg|450]] ^36a512 >[!Example] Ceiling Function > The *ceiling function* is a function with domain $\mathbb{R}$ and image $\mathbb{Z}$ defined as > $\lceil x\rceil = \min\{m\in\mathbb{Z}\mid m\ge x\}$ > Its output is the *smallest integer greater than or equal to* $x$. > > ![[CeilingFunction.svg|450]]