```Date: Mar 18, 2013 6:32 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <3df59ad9-d115-4db7-be04-333f0f87595b@k14g2000vbv.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 18 Mrz., 13:50, William Hughes <wpihug...@gmail.com> wrote:> > > So you take a set of lines that contains an unfindable line> > remove all the findable lines and end up with a set> > that contains an unfindable line, but no findable line ?!?> > If you remove every findable line, there cannot remain a findable> line, can it?> > But the more pressing question is: You construct a list such that> every line contains all preceding contents. You get ready, i.e., the> list contains all that it can contain. Nevertheless there is no line> that contains everything that the list contains.Works everywhere but in Wolkenmuekenheim.=========================================================================WM claimed:> The isomorphism is from |R,+,* to |R,+,*. Only in one case the> elements of |R are written as binary sequences and the other time as> paths of the Binary Tree. Virgil is simply too stupid to understand> that.everal flaws in WM's claim that the identity map on  induces a linear map on 2^|N.  WM's flaws in making that claim work include, but are not necessarily limited to:(1) not all members of |R will have any such binary expansions,  only those between 0 and 1, so that not all sums of vectors will "add up" to be vectors within his alleged linear space, and (2) some reals (the positive binary rationals strictly between 0 and 1) will have two distinct and unequal-as-vectors representations, requiring that some real numbers not be equal to themselves as a vectors, and(3) WM's method does not provide for the negatives of any of the vectors that he can form.On the basis of the above problems, and possibly others as well that I have not yet even thought of, I challenge WM's claim to have represented the set |R as the set of all binary sequences, much less to have imbued that set of all binary sequences with the structure of a real vector space or the showed the identity mapping to be a linear mapping on his set of "vectors".--
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