User robert paster - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T04:45:40Z http://mathoverflow.net/feeds/user/13397 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64156/discrete-continuous-digital-analog discrete continuous digital analog Robert Paster 2011-05-06T20:46:31Z 2011-05-06T20:46:31Z <p>Is the following statement, enclosed within quotation marks, true? If it is not, how can it most simply be changed so that it becomes true?</p> <p>"Mathematics is discrete when its domain must be integers, and is continuous when its domain may be real or complex numbers. Mathematics is digital when its range must be integers, and is analog when its range may be real or complex numbers."</p> http://mathoverflow.net/questions/57315/why-use-teichmuller-representatives Why use Teichmuller representatives? Robert Paster 2011-03-04T03:29:21Z 2011-03-04T06:01:36Z <p>In p-adic mathematics, what is the advantage of using Teichmuller representatives over using just the numbers 0,1,2,...,p-1 ?</p> <p>In either case, the norm is the same. In either case, all the points are in the center.</p> <p>Is is fair to say: "Teichmuller representives, just like the digits 0,1,2,...,p-1 , are just names of elements that are different in name but in no other characteristic. Although p-adic arithmetic seems more complex using Teichmuller representatives, more advanced mathematics is easier and more robust."</p> http://mathoverflow.net/questions/64156/discrete-continuous-digital-analog Comment by Robert Paster Robert Paster 2011-05-10T00:11:25Z 2011-05-10T00:11:25Z Is discrete mathematics equivalent to digital mathematics? Or is the term discrete mathematics specifically about mathematics for which input data (i.e., the domain) is limited to integers, whereas digital mathematics is specifically about mathematics for which output data (i.e., the range) is limited to integers?