```Date: Feb 4, 2013 5:14 PM
Author: Virgil
Subject: Re: WMytheology � 203

In article <ae2145db-0e20-429a-bef5-a6a423437230@k4g2000yqn.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 3 Feb., 23:04, fom <fomJ...@nyms.net> wrote:> > > > There is no sensible way of saying that 0.111... is more than every> > > FIS. And every FIS is in a line.> >> > Do you mean "is in some line"?> > What is s? In decimal it is 1/9. In binary it is 1. In paths or> strings of bits or decimals it does not exist!> >> > As in "there exists a line containing a given FIS"-> > There is not more than every FIS of 0.111... Not even all FIS. Here> you may see why:> 1) The set of all real numbers of the unit interval is (said to be)> uncountable.In ZF, and most other set theories in which the set of all naturals is allowed, the uncountability of the set of all subsets of the set of naturals is provable.> 2) An uncountable set has (infinitely many) more elements than a> countable set.Quite so, at least outside WMytheology.  > 3) Every real number has at least one unique representation as an> infinite binary string (some rationals have even two representations> but that's peanuts).But nothing guarantees that one can always find such a decimal or binary representation.> 4) In many cases the string cannot be defined by a finite word.That some reals are inaccessible is well known.> 5) Without loss of information the first bits of two strings, if> equal, need not be written twice.Without loss of information the FISs of uncountably many binary strings, if equal, need not be written twice.> 6) Application of this rule leads to the Binary Tree.Since WM's misunderstandings of of a Complete Infinite Binary Tree are pervasive and apparently incorrectable, from here on WM's stuff is even more junky than usual.--
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