Just like the title, is there a subsequence of $(\sin(n))_{n \in \mathbb{N}}$ that converge to 1 ? If it is, how to prove it? If it's possible, how to construct this subsequence? If it is not exist, how to prove it?
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Is $1$ a limit point of set $X={sin(n)}$? – Ashar Tafhim Feb 27 '17 at 16:56
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I'm pretty sure that ${sin(n)}$ is dense in $(-1,1)$. Edit: Yes, see http://math.stackexchange.com/questions/4764/sine-function-dense-in-1-1 – ThomasR Feb 27 '17 at 17:13