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# Superior limit of sin(n), and sin(n) always greater than epsilon>0.

1-1 For any $$\epsilon >0$$, Prove that there exists $$\sin { (n) } <\epsilon$$ where n is natural number. (If $$\epsilon >1$$, this is trivial.)

1-2 Prove that there are infinitely many natural number n that satisfies 1-1

2 Using above, prove that $$\limsup _{ n\rightarrow \infty }{\sin { (n) } } =1$$.

Note by Min-woo Lee
1 year, 8 months ago