\begin{definition}[Definition:Modulo Operation]
Let $x, y \in \R$ be real numbers.
Then the '''modulo operation''' is defined and denoted as:
:$x \bmod y := \begin{cases}
x - y \floor {\dfrac x y} & : y \ne 0 \\
x & : y = 0
\end{cases}$
where $\floor {\, \cdot \,}$ denotes the floor function.
\end{definition}