Date: Mar 21, 2013 4:53 AM
Author: Virgil
Subject: Re: Matheology � 224

In article 
WM <> wrote:

> If no line is necessary, then there is no necessary line.

While no particular line or even finite set of lines is necessary, what
is necessary is that both
1. That there is at least one line, and
2. For each line there is also a next longer line.


WM claims to know how to map bijectively the set of infinite binary
sequences, B, linearly to the set of reals and then map that image set
of reals linearly ONTO the set of all paths, P, of a Complete Infinite
Binary Tree.

But each binary rational in |R is necessarily the image of two sequences
in B but that one rational can then only produce one image in P, so the
mapping cannot be the bijection WM claims.

SO that WM is, as usual with things mathematical, wrong.