Virgil
Posts:
5,718
Registered:
1/6/11
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Re: Matheology � 233
Posted:
Mar 30, 2013 5:33 PM
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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.
It would if there were one, which there isn't!
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