\begin{definition}[Definition:Ceiling Function/Definition 2]
Let $x \in \R$ be a real number.
The '''ceiling function of $x$''', denoted $\ceiling x$, is defined as the smallest element of the set of integers:
:$\set {m \in \Z: x \le m}$
where $\le$ is the usual ordering on the real numbers.
\end{definition}