```Date: Jan 3, 2013 8:09 PM
Author: fom
Subject: Re: The Distinguishability argument of the Reals.

On 1/3/2013 3:53 PM, Virgil wrote:> In article> <a60601d5-24a2-4501-a28b-84a7b1e53bac@ci3g2000vbb.googlegroups.com>,>   WM <mueckenh@rz.fh-augsburg.de> wrote:>>> On 3 Jan., 14:52, gus gassmann <g...@nospam.com> wrote:>>>>> Exactly. This is precisely what I wrote. IF you have TWO *DIFFERENT*>>> reals r1 and r2, then you can establish this fact in finite time.>>> However, if you are given two different descriptions of the *SAME* real,>>> you will have problems. How do you find out that NOT exist n... in>>> finite time?>>>> Does that in any respect increase the number of real numbers? And if>> not, why do you mention it here?>> It shows that WM considerably  oversimplifies the issue of> distinguishing between different reals, or even different names for the> same reals.>>>>>> Moreover, being able to distinguish two reals at a time has nothing at>>> all to do with the question of how many there are, or how to distinguish>>> more than two. Your (2) uses a _different_ concept of distinguishability.->>>> Being able to distinguish a real from all other reals is crucial for>> Cantor's argument. "Suppose you have a list of all real numbers ...">> How could you falsify this statement if not by creating a real number>> that differs observably and provably from all entries of this list?>> Actually, all that is needed in  the diagonal argument is the ability> distinguish one real from another real, one pair of reals at a time.>One canonical name from another canonical name.
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