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

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 fom Posts: 1,968 Registered: 12/4/12
Re: The Distinguishability argument of the Reals.
Posted: Jan 3, 2013 7:38 PM

On 1/3/2013 7:52 AM, gus gassmann wrote:
> On 03/01/2013 8:58 AM, Zuhair wrote:
>> On Jan 3, 3:23 pm, gus gassmann <g...@nospam.com> wrote:
>>> On 03/01/2013 5:31 AM, Zuhair wrote:
>>>

>>>> Call it what may you, what is there is:
>>>> (1) ALL reals are distinguishable on finite basis

>>>
>>> > (2) Distinguishability on finite basis is COUNTABLE.
>>>
>>> What does this mean? If you have two _different_ reals r1 and r2, then
>>> you can establish this fact in finite time. The set of reals that are
>>> describable by finite strings over a finite character set is countable.
>>> However, not all reals have that property.

>>
>> I already have written the definition of that in another post, and
>> this post comes in continuation to that post, to reiterate:
>>
>> r1 is distinguished from r2 on finite basis <->
>> Exist n. n is a natural number & Exist d_n, k_n: d_n is the n_th
>> digit
>> of r1 & k_n is the n_th digit of r2 & d_n =/= k_n)

>
> 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?
>
> 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.
>
>

YES!

It sure is nice to see the problem in the definition.

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