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One of my friends asked me that is $\varliminf |nsinn|=0$? I think maybe it has some relations with Number theory, But I don't know how to solve it. If you know the answer, please tell me since it really puzzles me！

user49875
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    You might like to look at http://mathoverflow.net/questions/24579/convergence-of-sumn3-sin2n-1 . – Ben Barber Apr 22 '14 at 15:05
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    This question has been asked here before: http://mathoverflow.net/questions/144080/is-varliminf-n-rightarrow-infty-n-sin-n-0-correct-where-n-is-an – Joni Teräväinen Apr 22 '14 at 15:54

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