I have a set $X = [0, \infty)$ and two metrics:
$ d_1(x, y) = |x-y| $ $ d_2(x, y) = \left| \frac{x}{1+x} - \frac{y}{1+y} \right| $
I already showed that $d_1$ is equivalent to $d_2$. Now I have to show that $(X, d_2)$ is incomplete. As far as I have understood it I have to find a sequence that converges in both (because that depends on the topology that is the same) but not cauchy (since that depend on the metric).
What would such a sequence be?