# Definition:Farey Sequence

## Definition

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.

## Also see

• Results about the Farey sequence can be found here.

## Source of Name

This entry was named for John Farey.