On 23 Jan., 23:57, Virgil <vir...@ligriv.com> wrote: > In article > <56122973-de7e-4200-8780-cd571b20d...@n8g2000yqd.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 23 Jan., 19:56, Virgil <vir...@ligriv.com> wrote: > > > > > There it has meanwhile turned out ... But see it with your own eyes > > > > what you would not believe if I told you. > > > > We believe that the moderators ofhttp://math.stackexchange.comfound > > > the posting "of very low quality". > > > Here you can read it: > >http://www.hs-augsburg.de/~mueckenh/KB/complete%20tree.doc > > That paper starts with > > "How to distinguish between the complete and the incomplete infinite > binary tree? > > "How can we distinguish between that infinite binary tree that contains > only all finite initial segments of the infinite paths and the complete > infinite binary tree that in addition also contains all infinite path." > > But there is no difference between them anywhere outside of WMYTHEOLOGY. > > If there were, one would also have to have a difference between the set > which contains all finite initial segments of |N and |N itself
Correct. There is no difference. Therefore we can, in mathematics, use only the Binary Tree that contains all finite paths. More cannot be distinguished by nodes. It is the same set that contains all possible bit-sequences and is isomorphic to the set of all decimal fractions that can be applied in mathematics and in Cantor's diagonal argument. We can neither distinguish nor apply by digits more than all terminating decimal fractions. Therefore all that appears in Cantor's list is terminating decimal fractions. Therefore Cantor proves the uncountability of a countable set.