\begin{definition}[Definition:Modulo Operation/Modulo Zero]
Let $x, y \in \R$ be real numbers.
Let the modulo operation $\bmod$ be defined as:
:$x \bmod y := \begin {cases}
x - y \floor {\dfrac x y} & : y \ne 0 \\
x & : y = 0
\end {cases}$
Then:
:$\forall x \in \R: x \bmod 0 = x$
This can be considered as a '''special case''' of the modulo operation, but it is interesting to note that most of the results concerning the modulo operation still hold.
\end{definition}