Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 3:34 PM
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In article
<4ff1889f-baa9-43d7-98dd-f97cd3a8bad4@a8g2000vby.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 26 Dez., 09:43, Zuhair <zaljo...@gmail.com> wrote:
>
> > I want to note that I'm not claiming to have paradox in the formal
> > sense, but there is a kind of extreme counter-intuitiveness involved
>
> There is nothing depending on any intuition. The CIBT can be
> constructed in countably many steps, adding one node in every step and
> never removing anything. That means thare are not more than countable
> many different configurations.
In order to PROVE only countably many, one must be able to list them, or
at least show that they can be listed, since the very definition of
countability of a set requires that N can be surjected to it.
> Therefore not more than countably many
> different things can be distinguished by nodes.
Until you can prove listability, you have not proved countability.
> Where is any necessity
> for "intuition" in this clear mathematical argument?
You "intuit" but do not prove, that your sets satisfy the formal
definition of countability.
Or does WM claim a definition of countability other than the standard
one?
So much of WM's WMytheology is non-standard in actual mathematics, that
I would not be surprised if WM has his own private definition of
countability, that he hise the same way he hides the paths in his aleged
but unproven Complete Infinite Binary Tree.
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