# Definition:Group of Rationals Modulo One

## Definition

Define a relation $\sim$ on $\Q$ such that:

$\forall p, q \in \Q: p \sim q \iff p - q \in \Z$

Then $\left({\Q / \sim, +}\right)$ is a group referred to as the group of rationals modulo one.

That is, it is the quotient group $\Q / \Z$.