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Re: The Distinguishability argument of the Reals.
Posted:
Jan 3, 2013 8:52 AM
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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.
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