\begin{definition}[Definition:Farey Sequence]
The '''Farey sequence''' is a chain of subsets of the reduced rational numbers lying in $\Q \cap \closedint 0 1$.
For $Q \in \Z_{>0}$, the '''Farey set''' $F_Q$ is the set of all reduced rational numbers with denominators not larger than $Q$:
:$F_Q = \set {\dfrac p q: p = 0, \ldots, Q,\ q = 1, \ldots, Q,\ p \perp q}$
where $p \perp q$ denotes that $p$ and $q$ are coprime.
\end{definition}