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.

>

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