\begin{definition}[Definition:Group of Rationals Modulo One]
Define a relation $\sim$ on $\Q$ such that:
:$\forall p, q \in \Q: p \sim q \iff p - q \in \Z$
Then $\left({\Q / \sim, +}\right)$ is a group referred to as the '''group of rationals modulo one'''.
{{MissingLinks|The notation $\Q / \sim$ needs to be referenced.}}
That is, it is the quotient group $\Q / \Z$.
{{explain|$\Q$ and $\Z$ themselves are not groups as such until you give them an operation. Also, it needs to be demonstrated.}}
\end{definition}