Virgil
Posts:
4,479
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 3, 2013 4:45 PM
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In article
<bfa6347b-2078-4418-ac0b-815bc9e406ae@a15g2000vbf.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 3 Jan., 13:23, 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.
>
> Perhaps not all, but all that can be distinguished in a Cantor list.
The thing is that every such list by its own existence proves the
existence of reals not listed in it.
> >
> > > So we conclude that:
> >
> > > "The number of all reals distinguishable on finite basis must be
> > > countable".
> >
> > > Since ALL reals are distinguishable on finite basis, then:
> >
> > You seem to use "distinguishable" in two different ways.
>
> But you don't dare to say what these differences are.
It is WM who does not dare, as it would reveal his errors.
> >
> > Seeing your argument reminds me of the old chestnut about cats: A cat
> > has three tails. Proof: No cat has two tails. A cat has one tail more
> > than no cat. QED.
> >
> Unfortunately this joke has nothing to do with the question whether
> cats exist or whether matheologians can be intelligent.
WM certainly cannot be.
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