Hey I have to find a Cauchy-Sequence that converges in $(\mathbb{R} ,d_{|\cdot |})$ (absolute value as metric) and is still a Cauchy- Sequence with regards to a metric defined as $d(x,y):=|\frac{x}{1+|x|}-\frac{y}{1+|y|}|$ but doesn't converge in $(\mathbb{R},d)$. Has anyone got an idea or maybe a hint how i can proof that $(\mathbb{R},d)$ isn't a complete metric space?
2026-04-07 09:53:29.1775555609
Searching for a sequence that shows something isn't a complete metric space
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