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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 2:45 PM


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.



