User talk:Kephir/archive/2013/12

thanks
Hi, thanks for the figure at standard part function. Would it be possible to develop a cleaner version of the original figure as well? Tkuvho (talk) 14:54, 30 December 2013 (UTC)
 * Of course it would be possible. Keφr 15:30, 30 December 2013 (UTC)
 * The new figure is excellent, but the advantage of the original sketch is that it emphasizes the fact that "st" is a relationship between a pair of continua, which is less obvious from the new one. Tkuvho (talk) 15:35, 30 December 2013 (UTC)
 * Yes, but on the other hand the sketch did not show what the actual continua contain, and how the standard part function acts on them. Feel free to experiment with the TeX code, if you have an idea how to portray both. (Maybe we could have an arrow descend from the "infinitesimal microscope", directed at a point on the classical continuum.) Keφr 15:57, 30 December 2013 (UTC)
 * What I had in mind is simply the vertical projection, as indicated by the vertical arrow labeled "st" in the original sketch. Do you feel this is not self-explanatory? Perhaps an additional vertical arrow can be added over another point (say, root 2).  The microscope was intended to show that the "top" continuum contains infinitesimals. Tkuvho (talk) 16:13, 30 December 2013 (UTC)
 * Here is what I imagine someone looking on this image thinks: 'I have a thick line on the top, and a thin line on the bottom. And there is a bubble which shows that the thick line contains infinitesimals, while the thin line apparently does not. And a function called "st" maps between the two lines in some way. But where do the infinitesimals go?' Keφr 16:24, 30 December 2013 (UTC)
 * The page says early on that the standard part function "rounds off" each hyperreal to the nearest real. This implies that infinitesimals all go to zero.  Perhaps one could add this to the comment under the caption if we had the other sketch also.  Anyway once it is clear to the reader that the map is a vertical projection, there is nowhere for infinitesimals to go but 0, since they are positioned above zero.  As far as the bubble is concerned, we are pretty much assuming that the reader is familiar with Keisler's microscopes. After all we are not writing this page for Readers Digest users.  Tkuvho (talk) 16:35, 30 December 2013 (UTC)
 * Since all mathematics can be done with words, why have pictures at all? Anyway, it was easier to create a new image than to argue that it is not quite obvious that this is a projection. Also, I would be careful with making assumptions about who are we writing this for. Keφr 17:07, 30 December 2013 (UTC)
 * The new picture is great! Thanks. Tkuvho (talk) 17:21, 30 December 2013 (UTC)
 * P.S. Why don't we include both pictures? They emphasize different aspects of the function. Tkuvho (talk) 17:22, 30 December 2013 (UTC)
 * I think this one shows enough, and another picture would just add clutter. Keφr 17:37, 30 December 2013 (UTC)
 * Fine. Can you provide the code for generating this picture? Is this in latex? Tkuvho (talk) 08:43, 31 December 2013 (UTC)
 * Have you tried looking at the file page? Keφr 08:49, 31 December 2013 (UTC)