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lim sup X := sup x ∈ Y : x  is actually a Restrict place of  X displaystyle limsup X:=sup , xin Y:x text is usually a limit place of X , wouldn't be regarded as convergence.) Considering that the limit inferior is at most the limit excellent, the subsequent situations hold lim inf n → ∞ x n = ∞  indicates  lim n → ∞ x n = ∞ ,

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