In article <35ea24dc-1786-4dad-8c64-d8011ea2594c@x21g2000yqa.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 15 Jun., 22:45, Virgil <Vir...@home.esc> wrote: > > In article > > <f78b53d6-24d1-42e2-86bd-1dd0893b8...@q12g2000yqj.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 15 Jun., 16:06, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > > > > WM says... > > > > > > >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? > > > > > > r is computable *relative* to the list L of all computable reals. > > > > That is, there is an algorithm which, given an enumeration of computable > > > > reals, returns a real that is not on that list. > > > > > > In the theory of Turing machines, one can formalize the notion > > > > of computability relative to an "oracle", where the oracle is an > > > > infinite tape representing a possibly noncomputable function of > > > > the naturals. > > > > > We should not use oracles in mathematics. > > > > WM would prohibit others from doing precisely what he does himself so > > often? > > > > > A real is computable or not. My list contains all computable numbers: > > > > > 0 > > > 1 > > > 00 > > > ... > > > > > This list can be enumerated and then contains all computable reals. > > > > If that list is .0, .1, .00, ..., then it contains no naturals greater > > than 1. > > This list is the list of all words possible in any language based upon > any finite alphabet. The list is given in binary. All alphabets, all > languages and all dictionaries are contained in later, rather long but > finite lines. > Therefore this is a list of everything (that can meaningfully be > expressed).
Such a list never ends. > > This list does not allow for a diagonal, because that is a meaningless > concept. (That is proved in my list, in a later line.) > > Regards, WM
Is that like the typing monkeys eventually producing "Hamlet"?
Note that, unless there is a cap on the length of what is acceptable as a "word", or some other restrictionon what are allowed to be words, there can be no limit to the number of possible words
