# R and R^2 not quasi-isometric?

1. Oct 26, 2011

### nonequilibrium

Hello,

I'm reading a book on geometric group theory (and because this can be considered to be a part of multiple subsets of math, I chose to post it in the general math forum; correct me if this was incorrect).

One of the exercises in the book is "show that $\mathbb R$ and $\mathbb R^2$ are not quasi-isometric". This was shortly after the definition of quasi-isometry, so there's no real arsenal for it, so I suppose one has to prove it directly from definition (from contraposition?), but I don't really see it happening. Can anybody help me out?

EDIT: Sorry! Wrong forum... I just read the "MUST READ" and apparently questions like this should go into the homework questions forum, my apologies! Can somebody move it?