In article <email@example.com>, WM <firstname.lastname@example.org> 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.