On Sunday, May 4, 2014 2:52:48 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Sunday, 4 May 2014 00:25:49 UTC+2, Zeit Geist wrote: > > > Take Set of Aleph_0 Symbols, call it S. > > This set would not allow uncountably many finite expressions.
Are you talking about being able to be written on paper, of course not! But, that does not mean that it doesn't contain uncountably many expressions.
> > For Each Infinite Subset of S, say T, let the elements of T be the language L_T. > > There are Uncountably many Languages of the form L_T. > > If we wish to perform a mathematical dialogue, we have to agree on a language. We have to do so by a finite expression (otherwise we could never start). Therefore we have the choice between all languages that can be named by finite expressions. How many are there?
Just give me, in English, a Finite Definition that list All of the Definable Reals.