\begin{definition}[Definition:Congruence (Number Theory)/Modulo Zero]
Let $x, y \in \R$.
The relation '''congruence modulo zero''' is defined as:
:$x \equiv y \pmod 0 \iff x \bmod 0 = y \bmod 0 \iff x = y$ 
and:
:$x \equiv y \pmod 0 \iff \exists k \in \Z: x - y = 0 \times k = 0 \iff x = y$
This definition is consistent with the general definition of congruence modulo $z$ for any $z \in \R$.
\end{definition}