> 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 ... ?
