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## Main Question or Discussion Point

How to prove that the limit [tex]\lim_{n\to\infty}sin(n)^n[/tex] n integer towards infinity does not exist ?

If n is a real then it's obvious since we can take n=Pi/2*k k being an integer.

But if n is a integer then sin(n) is always smaller than 1, hence the power n should tend towards 0. I know this reasoning is wrong.

So is it not important the working set and we could use the reasoning on real set for n ?

Thanks.

If n is a real then it's obvious since we can take n=Pi/2*k k being an integer.

But if n is a integer then sin(n) is always smaller than 1, hence the power n should tend towards 0. I know this reasoning is wrong.

So is it not important the working set and we could use the reasoning on real set for n ?

Thanks.