On 4/1/2013 4:51 AM, WM wrote: > On 31 Mrz., 19:15, Virgil <vir...@ligriv.com> wrote: > >>>>> This was the question: In a list containing every rational: Is there >>>>> always, i.e., up to every digit, an infinite set of paths (rational >>>>> numbers) identical with the anti-diagonal? Yes or no? >> >>>> This is an equally valid question: What's the difference between a duck? >> >>> From the standpoint of matheology, perhaps. >> >> From the standpoint of logic and common sense, undoubtdly. >> >> Your question makes no sense > >> >>> Did you hitherto respond >>> in an unreasonable way because you misunderstood the question? >> >> Your questions assume conditions contrary to fact. > > You do not believe that a sequence or list of all rational numbers can > be constructed? Or do you not believe that the first n digits of all > these numbers in decimal representation can be compared with the first > n digits of the anti-diagonal number? Or is there something else you > do not understand? >
These questions are not equivalent to the senseless question above.
Even so, these questions are also senseless because belief has nothing to do with it.
Then there is...
> As explained before: > > > But note that the question also demonstrates WM's > > complete lack of understanding of the diagonal > > argument. > > > > He has been told time and time again that it is > > an argument scheme which only has application > > under certain assumptions. > > > > He chooses to believe otherwise for the agenda > > of his fanaticism. > > > > Suppose one is given a countable listing of > > the rationals (with the appropriate restriction > > on double representation) according to the > > infinite listing of an expansion. > > > > Suppose one performs a diagonalization on > > that listing. > > > > Is the resultant a rational number? No. > > > > What may be concluded? That the rational numbers > > do not exhaust the capacity of the algorithm > > to generate representations if that algorithm > > is to generate a representation for every > > rational number. > > > > Although the burden of proof lies with WM > > concerning the nature of the diagonal, it > > is a simple matter to understand if one > > uses a Baire space representation instead. > > > > In the Baire space, rationals are in correspondence > > with eventually constant sequences. Since, > > by construction, a list of Baire space rationals > > would exhaust all of the eventually constant > > sequences, the resultant of a diagonal argument > > could not have an eventually constant sequence > > unless the original premise had been false.