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

<1c0c41b2-58a5-43eb-ab37-5d5b35a96762@j9g2000vbz.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> 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.

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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.

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