On Tuesday, January 22, 2013 6:07:41 AM UTC-8, Seymour J. Shmuel Metz wrote: > In <lbGdnZWOCuemA2DNnZ2dnUVZ5rmdnZ2d@giganews.com>, on 01/21/2013 > > at 11:59 AM, "W. Dale Hall" <email@example.com> said: > > > > >Which statement is the "in fact, false" non-sequitur? > > > > "tangent vectors to different points on S^1 aren't quite identifiable > > with one another" > > > > >I maintain that my first statement is perfectly correct. > > > > You can maintain it all you want, but it remains false. > > > > >Otherwise, why would one ever worry about the whole machinery of vector bundles? > > > > Because in the general case you're not dealing with a flat affine > > connection. > > > > >A beginner needs to learn that the tangent bundle is something > > >other than a vector space; > > > > For which purpose S^2 is mopre suitable than S^1. > > > > >I suspect that the OP knows little to nothing about parallel transport. > > > > It might have been useful to mention it, stressing that what is true > > of S^1 is not true in general, even for S^2. > > > > >Again, I regard it as a pedagogical error to use machinery without > > >adequate justification > > > > I regard it as a pedagogical error to oversimplify.
Well, you seem to be criticizing a lot but you're not offering anything better; you're not being very constructive/helpful yourself. > > > > -- > > Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel> > > > > Unsolicited bulk E-mail subject to legal action. I reserve the > > right to publicly post or ridicule any abusive E-mail. Reply to > > domain Patriot dot net user shmuel+news to contact me. Do not > > reply to firstname.lastname@example.org