Re: Replacement of Cardinality

Le 28/08/2024 à 15:05, Moebius a écrit :

We'd better define:
  A set of ordinals is /Mückenheim complete/ iff each and every
         ordinal in the set (except 0)

0 is not an ordinal. See the recent olympic games. No starter number 0 has been seen, let alone won a medal.

has an immediate predecessor
         (which precedes it).
 Theorem: {0, 1, 2, 3, ... ω} is not Mückenheim complete. :-)

If ω exists, it proves the completeness of the whole set of ordinals. Why should any ordinals be missing? Because Cantor could not see them?

 Though it's not clear what's missing here. :-)

Think over that!
Regards, WM