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I am trying to see if a_n:={|Sin(n)|}, with n=1,2,... and | . | standard absolute value,

is convergent. I know the set {k.pi}, k=1,2,... is dense in [0,1] (pi is equidistributed mod1) , and we have that Sin(n)=Sin(n+pi), but it seems like {|Sinn|} is dense in [0,1], so that it cannot have a limit (i.e., a unique limit point). Any Ideas?