\begin{definition}[Definition:Integral Multiple/Real Numbers]
Let $x, y \in \R$ be real numbers.
Then $x$ is an '''integral multiple''' of $y$ {{iff}} $x$ is congruent to $0$ modulo $y$:
:$x \equiv 0 \pmod y$
That is:
:$\exists k \in \Z: x = 0 + k y$
\end{definition}