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Re: The Distinguishability argument of the Reals.
Posted:
Jan 3, 2013 12:38 PM
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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?
>
> 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?
Regards, WM
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