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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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Posts: 18,076
Registered: 1/29/05
Re: The Distinguishability argument of the Reals.
Posted: Jan 5, 2013 8:06 AM
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On 4 Jan., 22:36, "Jesse F. Hughes" <> 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.

Regards, WM

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