Definition:Farey Sequence

Definition

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

For $Q \geq 1$ the Farey set $F_Q$ is the set of all reduced rational numbers with denominators not larger than $Q$, that is:

$ 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.

Source of Name

This entry was named for John Farey.