Virgil
Posts:
4,486
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 3, 2013 4:53 PM
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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.
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