Using only the standard analytic properties of the sine function, but no particular definition of it,
what's a neat little proof that the sequence $\sin(n)$ diverges?
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I still wonder why people call "divergent" sequences that do not have a limit. It is a bounded sequence, how we may dare to call it "divergent"? – Jack D'Aurizio Sep 10 '15 at 22:41
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Divergent = not convergent, by standard definition? – Damian Reding Sep 10 '15 at 22:44
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It is not a universal definition. More or less, it is like to call "closed" sets that are not "open". Not a very wise terminology choice. – Jack D'Aurizio Sep 10 '15 at 22:46