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Topic: The Distinguishability argument of the Reals.
Replies: 11   Last Post: Jan 5, 2013 10:30 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: The Distinguishability argument of the Reals.
Posted: Jan 5, 2013 4:36 PM
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In article
<5c682c83-3374-4ccb-a12c-3aa42bb54286@u19g2000yqj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 4 Jan., 22:36, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>

> > Clearly, the set of reals is pairwise distinguishable but not totally
> > distinguishable.  But so what?

>
> A good question. A set distinguishable by such an n would necessarily
> be finite. Do you think that anybody, and in particular Zuhair, claims
> that |R is finite? Or did you miss this implication?
>
> A set S of infinite strings of digits (the God of matheology may
> present the strings without defining them in another way) is finitely
> distinguishable if for all x, y in S, if x != y then there is an m in |
> N (i.e., a finite index) such that x_m != y_m.


The "god" of WMytheology, namely WM himself, will insist that every such
potential string must have a finite definition in order to be thought
about at all.
>
> Regards, WM


Actually, real math suggests that there are reals so incredibly
inaccessible that finding the digit sequence representing one of them is
not possible.

In which case such numbers may well not be "finitely distinguishable".
--





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