\begin{definition}[Definition:Fractional Part]
Let $x \in \R$ be a real number.
Let $\floor x$ be the floor function of $x$.
The '''fractional part''' of $x$ is the difference:
:$\fractpart x := x - \floor x$
Beware, of course, not to get $\fractpart x$ confused with the singleton set containing $x$.
\end{definition}