Bruno Marchal skrev:
>
> To sum up; finite ordinal and finite cardinal coincide. Concerning
> infinite "number" there are much ordinals than cardinals. In between
> two different infinite cardinal, there will be an infinity of ordinal.
> We have already seen that omega, omega+1, ... omega+omega,
> omega+omega+1, ....3.omega, ... 4.omega .... ....omega.omega .....
> omega.omega.omega, .....omega^omega ..... are all different ordinals,
> but all have the same cardinality.
>
Was it not an error there? 2^omega is just the number of all subsets of
omega, and the number of all subsets always have bigger cardinality than
the set. So omega^omega can not have the same cardinality as omega.
--
Torgny
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Received on Tue Nov 20 2007 - 06:15:12 PST