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.