```Date: Dec 26, 2012 10:49 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Distinguishability of paths of the Infinite Binary tree???

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.And I showed that they cannot be distinguished by nodes.>> There are at least two counter-intuitive 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 matheologiansnot to believe in (and to call their thinking "complex" and a simpleand  clear contradiction "intuition"). No set of finite subsets of |Nexists, that was uncountable. Only a subset containing uncountablymany infinite subsets is uncountable. However, it is impossible todefine infinite subsets by themselves. You need always a finitedefinition. The set of all finite definitions however is countable. Nointuition requred.Cantor's and Hessenberg's "proofs" simply show that infinity is neverfinished and a complete infinite set is not part of sober thinking.You could be excused perhaps if the CIBT was the only contradiction ofyour belief. But there is a lot more, for instance this one:http://planetmath.org/?op=getobj&from=objects&id=12607Regards, WM
```