(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given (R^{+}, d), R-Real #

d= | ln(x/y) |

Show that this metric space is complete

2. Relevant equations

3. The attempt at a solution

Firstly, I know that to show it is complete I need to have that all Cauchy sequences in that space converge...

So I'm not 100% sure, but if I know I have to generalize so that it works for every Cauchy sequence, so can I find subsequences that converge, and then say that each sequence converges??? :S if so, how do I start this without picking specific cases, or can I pick a specific sequence in that space?

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# Show that a metric space is complete

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