Subsequences Converging to Limsup and Liminf of a Sequence
We construct subsequences of a sequence which converge to the limit superior and limit inferior respectively. The supremum approximation property allows us to find a terms in the original sequence which are as close as we wish to the supremum or infimum past a certain point in the sequence; this is the essential part of the proof.
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Видео Subsequences Converging to Limsup and Liminf of a Sequence канала Mike, the Mathematician
#mikethemathematician, #mikedabkowski, #profdabkowski
Видео Subsequences Converging to Limsup and Liminf of a Sequence канала Mike, the Mathematician
mike the mathematician prof dabkowski mike dabkowski math real analysis math 451 umich math 451 undergraduate real analysis limsup liminf limit superior limit inferior solutions abbott understanding analysis solutions rudin limsup examples liminf examples limsup definition liminf definition upper and lower limits limsup of function liminf of function limsup and liminf of sets limsup and liminf of sequence subsequence subsequence converging to limsup
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27 августа 2024 г. 17:40:35
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