If $f$ is a real-valued perform described on a set $Esubset mathbb R$ (or $subset mathbb R^k$), the upper and lower limits of $file$ at $x_0$ are denoted bywouldn't be regarded as convergence.) Since the Restrict inferior is at most the Restrict superior, the next circumstances keep lim?inf n ? ? x n = ? implies lim n ? ? x n = ? , lim?sup n ?
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