Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 223: AC and AMS
Posted:
Mar 18, 2013 7:13 PM


In article <e52645e6461d4e0dabcd015f5494d381@h14g2000vbe.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> It is an impudence to write so much nonsense that has not the least > relation to the topic and to expect that I read it.
WM, on the other hand also writes far more nonsense, but is often on his own topic, if not on the one under discussion.
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WM has several times claimed that the standard bijection from the set of all binary sequences to the set of all paths of a Complete Infinite Binary Tree is a linear mapping from the set of all binary sequences regarded as a linear space over R to the set of all paths of a CIBT.
While the mapping is easily shown to be bijective, it fails to be a linear mapping as WM describes it:
> 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 unequalasvectors 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, so his "space" does not qualify as a linear space in that way, either.
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 from one vector space to another.
Note that while WM's model doe not achieve what he claims for it, there is another model, which a reasonably competent mathematician should be able to find, which does make the mapping into an isomorphism of linear spaces.
It is a shame that someone so obviously of limited ability at mathematics as WM should feel himself so driven to try and correct his betters. 

