Is the set $S$ defined by $$S=\{\{n\pi\}:n\in \mathbb{Z}\}$$ dense in $(0,1)$?
Here $\{x\}$ denotes the fractional part of $x$
I cannot proceed ahead after recalling the definition of dense sets. I cannot find any way to solve this problem.
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There is a proof in this answer; the result is true for all irrationals, not just $\pi$. – Brian M. Scott Jun 15 '20 at 17:29
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Check Kronecker's Approximation Theorem. – rtybase Jun 15 '20 at 19:36