\begin{definition}[Definition:Set of Residue Classes/Least Absolute]
Let $\eqclass a m$ be the residue class of $a$ (modulo $m$).
Except when $r = \dfrac m 2$, we can choose $r$ to be the integer in $\eqclass a m$ which has the smallest absolute value.
In that exceptional case we have:
: $-\dfrac m 2 + m = \dfrac m 2$
and so:
: $-\dfrac m 2 \equiv \dfrac m 2 \pmod m$
Thus $r$ is defined as the '''least absolute residue''' of $a$ (modulo $m$) {{iff}}:
: $-\dfrac m 2 < r \le \dfrac m 2$
\end{definition}