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Topic:
No John Gabriel, an infinite sum is a limit and 0.333... is indeed 1/3. Plus several other misconceptions Gabriel has
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Last Post:
Oct 4, 2017 2:58 PM




Re: No John Gabriel, an infinite sum is a limit and 0.333... is indeed 1/3. Plus several other misconceptions Gabriel has
Posted:
Oct 4, 2017 2:58 PM


Remark: It would surprise me, if there were some circular constructions of the reals floating around.
Circular is not necessarely bad, for example if you add some minimality criteria to a montone operator,
you might get unique least fixpoints, etc.. etc.. Here is a paper discussing reals and circularity:
Comparing inductive and circular definitions: parameters, complexity and games http://www.illc.uva.nl/Research/Publications/Reports/PP200407.text.pdf
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.



