But maybe there is somewhere a more down to earth paper, that shows a inductive real construction?
Is this possible? Does Cauchy or Dedekind have an inductive aspect?
Am Mittwoch, 4. Oktober 2017 20:46:01 UTC+2 schrieb burs...@gmail.com: > Yes, this wouldn't work somehow, it > would be circular, not foundational: > > _ > / \ > real | > / \_/ > rational > > Running into case 1 or 2 of the > Münchhausen trilemma. > > Am Mittwoch, 4. Oktober 2017 20:41:08 UTC+2 schrieb Markus Klyver: > > And no, we don't define real numbers as limits of Cauchy sequences. That's an other strawman and completely illogical. We can, however, define a real number as an equivalence class of rational Cauchy sequences. An equivalence class is not a limit. An equivalence class is a set of equivalent elements under a certain equivalence relation.