On Friday, 2 May 2014 21:04:55 UTC+2, Virgil wrote:
> > But we know that every expression that can appear in eternity in the whole, > > possibly infinite, universe belongs to a countable set. > > > > But the setof all subsets, or power set, is of provably greater > cardinality then the set itself, so the existence of even one countably > infinite set requires the existene of uncountably infinite sets.
Then the only conclusion is that countability is nonsense. > > > > > Therefore also every > > expression that can appear in the mathematical discourse belongs to a > > countable set. > > > > That may be true in WMytheological discourse,
It is true everywhere in set theories with the notion of countability:
a b aa ab ba bb aaa ...
> > Nothing that can appear in this discourse, which *is* mathematics, can be > > uncountable. >
> So that WM requires existence of sets for which there are no sets of all > subsets?
All that exists in mathematics is (at most) countable. > > > > > > We do *not* need any definition of "definition".