# Math Help - special metric

1. ## special metric

Hi!
I have one interesting question. Is it possible to find a special metric that a space R is not complete by this metric? I now that the space R is complete with usual Euclidean metric but I don't now about other metrics in this space.

2. ## Re: special metric

Put $d(x,y)=|e^x-e^y|$. It's a metric on $\mathbb R$, which is topologically equivalent to the usual metric, but the sequence $\{-n\}$ is a Cauchy sequence which is not convergent.