I have to say Plato, I did think that was a tiny bit arrogant to ask. It should be obvious, but better to ask than to just assume!
If you wanna formalize why there can be no convergent subsequence, we can assume to the contrary. Let [tex]s_{n} = 2\pi n[/math[ and assume that there is a subsequence
such that given
, there exists
such that
implies
, where
is the finite number that we suppose the subsequence will converge to. And so this means for all
,
(assume that
because if it wasn't, then clearly after some point the sequence would have to be negative). But since
, we know for
all ,
, and so rises the contradiction.