most recent 30 from http://mathoverflow.net 2013-05-25T02:15:15Z http://mathoverflow.net/feeds/user/20204 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/84025/how-to-write-popular-mathematics-well/96556#96556 Davey 2012-05-10T09:20:01Z 2012-05-10T09:20:01Z

<p>I think the answer is simple. </p> <p>1) Read, and as widely as possible.</p> <p>2) Write, as much as possible.</p> <p>3) Compare what you learn (what works and doesn't) in reading to writing and vice versa.</p>

http://mathoverflow.net/questions/75680/when-does-the-set-of-isometries-form-a-group/84383#84383 Davey 2011-12-27T13:35:35Z 2011-12-27T13:35:35Z

<p>Not sure how to comment, but it seems that some concept of dimension is important here. Things clearly break down for infinite dimensional spaces, but a finite dimensional space cannot have a lower dimensional subspace that is isomorphic. </p>

http://mathoverflow.net/questions/75680/when-does-the-set-of-isometries-form-a-group/84383#84383 Davey 2011-12-27T19:46:31Z 2011-12-27T19:46:31Z

That is unduly harsh. I wanted to make this a comment, as it is clearly not a full answer, but cannot as I am new to the site. In the example you give the non-surjective isometry is not to a lower dimensional subspace, such examples need to be considered, but it does not make anything I said false.