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