Should I prove that there exists $\epsilon$ such that for every $M \in R$ exist $x>M$ for which $\lvert \langle x \rangle - \frac{1}{2} \rvert \ge \epsilon?$ And if so, how do I do it?
2026-03-25 11:24:05.1774437845
Prove with $\epsilon$, M that $\lim\limits_{x \to \infty} \langle x \rangle$ $\ne$ $\frac{1}{2}$
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You take $\epsilon=0.25$ (for example) and $x=n$ with natural $n>M$.