I am wondering how to prove that the supremum of the following sequence is 1 $$a_n=\sin (n)$$
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The Kronecker density theorem. Look at this page: http://math.stackexchange.com/questions/484131/what-is-sup-sinn – Sarvesh Ravichandran Iyer Jan 19 '17 at 23:53
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Actuually, ${\sin n\mid n\in\mathbf N}$ is dense in $[-1,1]$. – Bernard Jan 19 '17 at 23:59