  A set $A$ is an $(r,\ell)$-approximate group in the additive abelian group
$G$ if $A$ is a nonempty subset of $G$ and there exists a subset $X$ of $G$
such that $|X| \leq \ell$ and $rA \subseteq X+A$. The set $A$ is an asymptotic
$(r,\ell)$-approximate group if the sumset $hA$ is an $(r,\ell)$-approximate
group for all sufficiently large integers $h$. It is proved that every finite
set of integers is an asymptotic $(r,r+1)$-approximate group for every integer
$r \geq 2$.
