Category:Definitions/Farey Sequences

This category contains definitions related to Farey Sequences.
Related results can be found in Category:Farey Sequences.

A 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.