In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 2 Feb., 09:57, fom <fomJ...@nyms.net> wrote: > > On 2/1/2013 9:48 AM, WM wrote: > > > > > > > > > > > > > On 1 Feb., 16:35, William Hughes <wpihug...@gmail.com> wrote: > > >> Let P(n) be > > >> 0.111... is not the nth line > > >> of > > > > >> 0.1000... > > >> 0.11000... > > >> 0.111000... > > >> ... > > > > >> Clearly for every natural number n > > >> P(n) is true. > > > > >> This means there is no natural > > >> number m for which P(m) is true. > > > > >> It is not simply that we cannot find m, > > >> we know that m does not exist. > > > > > More. We know that P(n) = 0.111... = 1/0 does not exist as an > > > actually infinite sequence of 1's. > > > > Hmm.... > > > > As I watch you make these arguments, it occurs to me... > > > > What proof do you have that some sequence is not infinitely > > long? > > Even with no regard to Tristram Shandy who disproves actual infinite, > we can say: The sequence for 1/9 = 0.111... cannot have indices that > differ from all indices of its finite approximations. So you cannot > distinguish 0.111... by looking at digits from its finite > approximations. And you cannot use it in any discourse because every > message is finite and needs an endoffile signal to be meaningful.
Either the sequence 0.111... has a last digit or beyond each digit there is another. Tertium Non Datur, at least not outsiede WMytheology . > > Concluding: The property that a sequence of digits does not end cannot > be obtained from its digits. (Remember, 0.111... is not a sequence of > digits but is only a rule to construct a sequence of digits. The rule > yields the sequence, but the sequence does not yield the rule.) > > That means in mathematics