In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 31 Jan., 15:27, forbisga...@gmail.com wrote: > > > The rational 1/3 > > doesn't have a finite decimal expansion. None the less it is > > distinguishable > > from every rational other than 1/3 at some place in the expansion > > and only the infinite expansion can be calculated to be 1/3. > > If you are so sure about that than you should be able to find out > whether 1/3 is among the paths that I have used to construct the > complete infinite Binary Tree. Does it in fact differ from the union > of all its finite initial segments > 0.01 > 0.0101 > 0.010101 > ... > ?
But in WMytheology it is not allowed that one have a binary with infinitely many finite initial segments, since that would require an actual infinity of them.
And note that each of those finite initial segments is also an infinite sequence having all but a finite number of digits being 0. --