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Topic: The Distinguishability argument of the Reals.
Replies: 1   Last Post: Jan 5, 2013 4:32 PM

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Jesse F. Hughes

Posts: 9,776
Registered: 12/6/04
Re: The Distinguishability argument of the Reals.
Posted: Jan 5, 2013 4:32 PM
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WM <> writes:

> 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?

After posting, I came to that conclusion as well. Thus, I've no idea
what Zuhair means when he says that distinguishability implies
countability. (He said that it means the set of finite initial segments
is countable, but since this does not contradict the uncountability of
R, I don't know why he thinks this is paradoxical.)

Again, let's let Zuhair clarify precisely what his argument is. I just
don't see it.

"This is based on the assumption that the difference in set size is what
makes the important difference between finite and infinite sets, but I think
most people -- even the mathematicians -- will agree that that probably
isn't the case." -- Allan C Cybulskie explains infinite sets

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