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Answer to Question #7834 in Real Analysis for Mike
Question #7834
Show that it is possible for a sequence to have no convergent subsequences at all.
Expert's answer
Let's consider the next permanently ascending sequence: {1, 1+1, 1+1+1, ...}. Obviously, this sequence has no convergent subsequences. So, it is possible for a sequence to have no convergent subsequences.
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#340153 on Dec 2023
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