Am Donnerstag, 5. Dezember 2013 18:30:40 UTC+1 schrieb Zeit Geist:
> > Could you give a model of ZFC at all? > > > I give two. > > ZFC + V=L > > ZFC + "There Exists an Inaccessible Cardinal." >
Ah, ZFC is a model of ZFC? Interesting. >
> > Look: Every definition in mathematics is a finite word in English or any formal language. The set of all possible finite words in English or any formal language is countable. Proof left as an exercise. > > > A subset of a countable set is countable. > > And the Set of All Definitions, when properly And Logically implemented, cannot be put into Bijection with N.
What do we learn from that fact? (It is a fact.) Either a subset of a countable set can be uncountable. Or: Countability is a self-contradictory notion.