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 ${n_1,n_2,ldots,} otin mathcal{I}$). The analogous characterization holds also for $mathcal{I}$-cluster points.
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