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.