  Let $\Lambda$ be a numerical semigroup with embedding dimension $e(\Lambda)$.
Define $c(\Lambda)$ to be one plus the largest integer not in $\Lambda$, and
define $c'(\Lambda)$ to be the number of elements in $\Lambda$ less than
$c(\Lambda)$. It was asked by Wilf whether $\frac{c'(\Lambda)}{c(\Lambda)} \ge
\frac{1}{e(\Lambda)}$ always holds. We prove an asymptotic version of this
conjecture: we show that for a fixed positive integer $k$ and any $\epsilon >
0$, the inequality $\frac{c'(\Lambda)}{c(\Lambda)} \ge \frac{1}{k} - \epsilon$
holds for all but finitely many numerical semigroups $\Lambda$ satisfying
$e(\Lambda) = k$.
