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Topic: The Distinguishability argument of the Reals.
Replies: 83   Last Post: Jan 7, 2013 12:58 AM

 Messages: [ Previous | Next ]
 gus gassmann Posts: 60 Registered: 7/26/12
Re: The Distinguishability argument of the Reals.
Posted: Jan 4, 2013 7:36 AM

On 03/01/2013 5:53 PM, Virgil wrote:
> In article
> 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.

Exactly. The only reals that matter to Cantor's argument are the
*countably* many that are assumed to have been written down. There is no
need (nor indeed an effective way) to distinguish the constructed
diagonal from *all* the potential numbers that could have been
constructed that are not on the list, either. Any *one* number not on
the list shows that the list is incomplete and thus establishes the
uncountability of the reals.

Date Subject Author
1/1/13 Zaljohar@gmail.com
1/2/13 mueckenh@rz.fh-augsburg.de
1/2/13 Virgil
1/3/13 Virgil
1/3/13 Zaljohar@gmail.com
1/3/13 gus gassmann
1/3/13 Zaljohar@gmail.com
1/3/13 gus gassmann
1/3/13 Zaljohar@gmail.com
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 fom
1/4/13 Zaljohar@gmail.com
1/4/13 fom
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 fom
1/3/13 Virgil
1/4/13 gus gassmann
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/4/13 Virgil
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/4/13 Virgil
1/4/13 gus gassmann
1/4/13 ross.finlayson@gmail.com
1/5/13 Virgil
1/5/13 ross.finlayson@gmail.com
1/5/13 Virgil
1/5/13 fom
1/5/13 ross.finlayson@gmail.com
1/6/13 fom
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/7/13 ross.finlayson@gmail.com
1/7/13 Virgil
1/3/13 fom
1/3/13 fom
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/6/13 Virgil
1/6/13 fom
1/6/13 Virgil
1/6/13 fom
1/6/13 ross.finlayson@gmail.com
1/4/13 Virgil
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 forbisgaryg@gmail.com
1/3/13 Virgil
1/4/13 Zaljohar@gmail.com
1/4/13 Virgil
1/4/13 Zaljohar@gmail.com
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/5/13 Virgil
1/4/13 Virgil
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/4/13 Virgil
1/2/13 Bill Taylor