# Cauchy sequence nonconvergent in general metric space

I know that a sequence in $\mathbb{R}^d$ is Cauchy iff it is convergent, and also convergent sequences are Cauchy in a general metric space. How does the converse fail in a general metric space? In other words, what part of the proof that Cauchy sequences in $\mathbb{R}^d$ are convergent cannot be generalized to an arbitrary metric space?

The sequence $$\left\{\frac1n\right\}_{n=1}^\infty$$ is Cauchy, but not convergent, in $(0,\infty)$ equipped with the standard metric.
• Ah, B.W. only holds in $\mathbb{R}^d$ – b_pcakes Nov 7 '16 at 8:42