MathProblemsBank

19.1.1.4 Properties of metric spaces

Problem: Let the metric on \( \mathbb{R} \) be \( \rho(x, y)=\mid \tan ^{-1} x- \) \( -\tan ^{-1} y \mid \). Prove that the obtained space is not complete. Indication: consider the sequence \( x_{n}=n \).