In article <39a1fada-4fc1-4214-a858-df63a2444a7c@a30g2000yqn.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 15 Jun., 18:49, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > > WM says... > > > > > > > > > > > > > > > > >On 15 Jun., 16:18, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > > >> Peter Webb says... > > > > >> >"WM" <mueck...@rz.fh-augsburg.de> wrote in message > > >> >news:62ae795b-1d43-4e1f-8633-e5e2475851aa@x21g2000yqa.googlegroups.com.. > > >> >. > > >> >> On 15 Jun., 12:26, stevendaryl3...@yahoo.com (Daryl McCullough) > > >> >> wrote: > > > > >> >>> (B) There exists a real number r, > > >> >>> Forall computable reals r', > > >> >>> there exists a natural number n > > >> >>> such that r' and r disagree at the nth decimal place. > > > > >> >> In what form does r exist, unless it is computable too? > > > > >> >Of course its computable. > > > > >> No, it's computable *relative* to the list of all computable reals. > > >> But that list is not computable. > > > > >That is nonsense! > > > > >The list of all definitions is possible and obviously contains all > > >definitions of real numbers. > > > > I was talking about the list of all *computable* reals. There are > > definable reals that are not computable, and Cantor's proof shows > > how to define one. > > No, it does not show that because it is impossible to define a real by > an infinite definition. A Cantor-list without a finite definition > however is an infinite definition. > > Sensible definitions are finite.
As far as I am aware, "sensible" has no mathematical meaning at all.
There is nothing in mathematics which requires anything to be sensible.
> So you explanation is nonsense in highest degree.
Not even up to WM's usual level of nonsense. > > > > You can similarly get a list of all definable reals for a specific > > language L. > > Every real that is definable in a specific language is definable in > another specific language. The set does not grow or shrink or change > when the language is changed.
That is a statement that requires proof, which WM, as usual, has not provided.
There are, I believe, in both mathematics and logic, "Languages" which are proper "sub-languages" of other languages so that things expressible in a super-language are not always expressible in its sub-languages.
