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  "body": "\n## Summary\n\nA sequence converges statistically to $L$ when, for every $\\varepsilon \u003e 0$, the indices $n$ with $\\abs{x_n - L} \\ge \\varepsilon$ form a set of [[natural density|RVG9Z8NYA6]] zero.\nSo the sequence may stray from $L$ infinitely often, but only on a sparse set of indices.\nEvery convergent sequence converges statistically to its limit, but not conversely.\nFor bounded sequences, statistical convergence to $L$ is equivalent to [[strong Cesàro summability|750MCA763X]] to $L$ with exponent $1$.\n\n## Explanations\n\n### L1 human\n\nOrdinary convergence allows only finitely many terms to be far from the limit.\nStatistical convergence allows infinitely many, as long as they become rarer and rarer, so that their proportion among the first $n$ terms tends to $0$.\nFor example, the sequence that is $1$ at perfect squares and $0$ elsewhere converges statistically to $0$, since there are only about $\\sqrt{n}$ squares up to $n$.\nIt does not converge in the usual sense, because the ones never stop.\n",
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