Date: Feb 4, 2013 5:14 PM
Subject: Re: WMytheology � 203
WM <firstname.lastname@example.org> 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)
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
> 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.