I am wondering how to prove that the supremum of the following sequence is 1 $$a_n=\sin (n)$$
Supremum of the sequence $\sin (n)$
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sequences-and-series
convergence
supremum-and-infimum
cauchy-sequences
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0The Kronecker density theorem. Look at this page: http://math.stackexchange.com/questions/484131/what-is-sup-sinn – 2017-01-19
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0Actuually, $\{\sin n\mid n\in\mathbf N\}$ is dense in $[-1,1]$. – 2017-01-19