  We show that an ideal $\mathcal{I}$ on the positive integers is meager if and
only if there exists a bounded nonconvergent real sequence $x$ such that the
set of subsequences [resp. permutations] of $x$ which preserve the set of
$\mathcal{I}$-limit points is comeager and, in addition, every accumulation
point of $x$ is also an $\mathcal{I}$-limit point (that is, a limit of a
subsequence $(x_{n_k})$ such that $\{n_1,n_2,\ldots,\} \notin \mathcal{I}$).
The analogous characterization holds also for $\mathcal{I}$-cluster points.
