Re: Replacement of Cardinality

Le 28/08/2024 à 15:05, Moebius a écrit :
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We'd better define:
  A set of ordinals is /Mückenheim complete/ iff each and every
         ordinal in the set (except 0)

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0 is not an ordinal. See the recent olympic games. No starter number 0 has been seen, let alone won a medal.
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has an immediate predecessor
         (which precedes it).
 Theorem: {0, 1, 2, 3, ... ω} is not Mückenheim complete. :-)

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If ω exists, it proves the completeness of the whole set of ordinals.