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. Only finite initial segements exist in potential infinity.
Compare the Binary Tree. There is no path for 1/9 that could be distinguished from all its approximations.