Virgil
Posts:
9,012
Registered:
1/6/11


Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 6:03 PM


In article <c3b5cefe1a77479caddabf1015f5ab78@g6g2000vbk.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 26 Dez., 13:24, gus gassmann <g...@nospam.com> wrote: > > On 26/12/2012 7:29 AM, Zuhair wrote: > > > > > > > > >> Depends on the level of distinguishability at issue. > > > > >> For any finite set of such strings, finite initial segments suffice to > > >> distinguish all of them from each oterhbut for at least some infinite > > >> set, no finite set of finite initial segments suffices. > > > > > Yes but a countable set of them suffices! no? > > > > Of course. And how many such countable sets are there? Cantor showed > > that there are uncountably many. > > Cantor showed that by digits or nodes.
Since while sets may have members they need not ever contain either digits or nodes, Cantor did no such thing.
> And I showed
The only thing you evern sow is your own ignorance. > > > > There are at least two counterintuitive notions when dealing with > > infinities: There is an infinite set, each of whose elements are finite > > (viz. the sequence of initial segments {{1}, {1,2}, {1,2,3}, ...}; and > > the set of all countable subsets of a countable set is uncountable. The > > only thing this shows is that intuition is sometimes insufficient to > > grasp complex things. > > No, it shows that there is no nonsense great enough for matheologians
Like WM
> not to believe in
> No set of finite subsets of N exists, that was uncountable. Do you mean that now there are some which have now become uncountable? > Only a subset containing uncountably > many infinite subsets is uncountable.
Right! And in ZFC, for example, such sets must exist. > > Cantor's and Hessenberg's "proofs" simply show that infinity is never > finished and a complete infinite set is not part of sober thinking.
Thinking about infiniteness certainly makes WM extremely unsober. 

