Am Dienstag, 3. Dezember 2013 18:53:38 UTC+1 schrieb Zeit Geist:
> > Where in the Axiom Set for the Real Numbers are "Defined Numbers" mentioned?
They are not mentioned because undefined numbers are not numbers. For undefined numbers we cannot find out the sum or, in Cantor's list, the digit a_nn. > > > > Where in you posts have you given a a Formal Conception of "Definable Numbers"?
There is no formal defintion because formal language is incapable of many necessary things. But every definable number is definable by a finite word that does not defina another number.
> > > No. ZFC has uncountability. Definable numbers have not. > > > > Could you give an example of a Model of ZFC in which all Real Numbers are definable and that contains a Bijection between N and R. >
Could you give a model of ZFC at all? > > > > > Some Models contain them, and some don't > > > > > > The latter must be countable. > > > > Really? Show me!
> You seem so convinced of it. > > You should be able to Prove it.
I did. You seem to have a very bad memeory.
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.