In article <ff6dnb5sjeDL1crMnZ2dnUVZ_ridnZ2d@giganews.com>, fom <fomJUNK@nyms.net> wrote:
> On 3/30/2013 8:38 AM, WM wrote: > > On 29 Mrz., 19:34, Virgil <vir...@ligriv.com> wrote: > > > >> > >>> So we have established the fact that an irrational number has no node > >>> of its own. > >> > >> No number in any infinite binary tree has any node "of its own", as > >> every node has two child nodes belonging to necessarily different > >> numbers. > > > > That is correct, but only establishes the fact that no actually > > infinite path can be distinguished from all rational paths as should > > be possible in a Cantor-list - but is not. > > > > WM failed the science lesson again today. > > The Cantor argument is an argument scheme. > > It presupposes a standard, classical use of > of the quantifier "all". > > WM has never defined his non-standard uses > for the word "all". It has no agreed upon > usage. It is meaningless by WM's own standards > of meaning through pragmatic agreements between > language users. > > By definition, all paths in the complete infinite > binary tree are infinite whether or not they > become eventually constant. > > Any purported countable listing of all the paths > of that tree will result in a successful > defeat of the claim by a Cantor argument.