Date: Jan 3, 2013 8:09 PM
Subject: Re: The Distinguishability argument of the Reals.
On 1/3/2013 3:53 PM, Virgil wrote:
> In article
> WM <email@example.com> 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.