On Saturday, 3 May 2014 10:25:00 UTC+2, Zeit Geist wrote: > On Saturday, May 3, 2014 12:48:09 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > > > On Friday, 2 May 2014 23:20:55 UTC+2, Zeit Geist wrote: > > > > > > > Can you please provide a Countable List > > > > > > Every list is countable. > > > > > > > of ALL Finitely Definable Real Numbers? > > > > Remember, this List must have a Finite Definition. > > > > > > I use set theory. All finite expressions in all possible (non-formal and formal) languages form a countable set. This is undisputed except by extreme-matheologians who wish to create uncountably many languages or uncountable alphabets. I do not argue with them. > > > > > > > But there are Uncountable many Languages.
As I said, I do not discuss with fools.
> Just pick one.
Impossible without a dictionary. A language has to be known by the user. For that sake there has to be a dictionary. You can costruct it, if you like, but there can never more than a finite number of languages exist. > > > > > > A real number is defined by (at least) one or (frequently) more of those expressions. Therefore all real numbers form a subset of the set of all finite expressions. According to ZF set theory a subset of a countable set is countable. >
> > But how do you know that that countable subset is Finitely Definable?
I do not know it. I know that every subset of a countable set is countable in ZF.
> > Give an Explicit Definition of that List.
Why? I show that the assumption of infinite lists, i.e., of bijections with |N, lead to contradictions with the rule that subsets cannot have larger cardinality than sets.