Talk:Quasi-isometry

Displayed lattice not actually quasi-isometric to the plane

The article contains this captioned image:

This lattice is quasi-isometric to the plane

However, the lattice in the image is bounded, and thus cannot be quasi-isometric to the plane, which is unbounded.

If it were bounded, it would not be a lattice. The more reasonable reading is that it is intended to be only a small part of a lattice, enough for the reader to understand what the rest looks like. We cannot actually draw all of an infinite lattice with a finite number of pixels. —David Eppstein (talk) 03:49, 31 March 2017 (UTC)[reply]

Why is there an additive constant B in the definition?

I wonder if an example could be added to the article to show the necessity of including the additive constant B in the definition of quasi-isometry. 2601:200:C000:1A0:21A7:B740:95E6:BA8D (talk) 18:11, 5 September 2021 (UTC)[reply]

The additive constant is here to allow quasi-isometries that are not necessarily continous, for example the map defined by the integer part from the reals to the integers is a quasi-isometry. I think more involved examples would be a bit cumbersome to define dproperly but the Švarc–Milnor lemma should probably be mentioned there. If nobody has a better idea I'll edit the article to add something like this. jraimbau (talk) 10:25, 6 September 2021 (UTC)[reply]