\begin{definition}[Definition:Congruence (Number Theory)/Modulo Operation]
Let $z \in \R$.
Let $\bmod$ be defined as the modulo operation:
:$x \bmod y := \begin{cases}
x - y \floor {\dfrac x y} & : y \ne 0 \\
x & : y = 0
\end{cases}$
Then '''congruence modulo $z$''' is the relation on $\R$ defined as:
:$\forall x, y \in \R: x \equiv y \pmod z \iff x \bmod z = y \bmod z$ 
The real number $z$ is called the '''modulus'''.
\end{definition}