Definition:Farey Sequence

Definition
The Farey sequence is a chain of subsets of the reduced rational numbers lying in $\Q \cap \left[{0 \,.\,.\, 1}\right]$.

For $Q \in \Z_{>0}$, the Farey set $F_Q$ is the set of all reduced rational numbers with denominators not larger than $Q$:


 * $F_Q = \left\{{\dfrac p q: p = 0, \ldots, Q,\ q = 1, \ldots, Q,\ p \perp q} \right\}$

where $p \perp q$ denotes that $p$ and $q$ are coprime.