Date: Mar 17, 2013 8:11 PM Author: ross.finlayson@gmail.com Subject: Re: Matheology § 224 On Mar 17, 4:59 pm, Virgil <vir...@ligriv.com> wrote:

> In article

> <ba28932b-ac48-4567-8e5c-a7e9262f8...@z4g2000vbz.googlegroups.com>,

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 17 Mrz., 21:48, Virgil <vir...@ligriv.com> wrote:

>

> > > Mathematical truth is independent of time.

>

> > In fact??? Amazing! After Cantor's list has been diagonalized, it is

> > possible to include all diagonals into the list. But someone has

> > forbidden to change the list after time t_0 when the diagonalizers

> > start to do their work.

>

> Why does WM claim that after what WM calls "Cantor's list" has been

> diagonalized, he can include all anti-diagonals, when it is always

> possible to find others that have been so far overlooked?

>

> After each anti-dagonal of any list is found, prefix it to that list and

> then the anti-diagonal to the new list is not in the new list or the old

> sub-list.

>

> This procedure always finds new lines which are non-members of any of

> the prior lists of lines including all lines of any original list and

> all previously found anti-diagonals of those prior lists.

>

> WM is just not paying attention!

>

> ######################################################################

>

> WM has frequently claimed that HIS mapping from the set of all infinite

> binary sequences to the set of paths of a CIBT is a linear mapping.

>

> In order to show that such a mapping is a linear mapping, WM would first

> have to show that the set of all binary sequences is a linear space

> (which he has not done and apparently cannot do) and that the set of

> paths of a CIBT is also a vector space (which he also has not done and

> apparently cannot do) and then show that his mapping, say f, satisfies

> the linearity requirement that f(ax + by) = af(x) + bf(y),

> where a and b are arbitrary members of the field of scalars and x and y

> and f(x) and f(y) are arbitrary members of suitable linear spaces.

>

> While this is possible, and fairly trivial for a competent mathematician

> to do, WM has not yet been able to do it.

>

> But frequently claims already to have done it.

> --

With whatever expansions EF would have, the binary antidiagonal is at

the end. Obviously, prepending .111... to the beginning is not then

EF (the function modeled by n/d, n->d, d->oo).

Bo-ring. Virgil my good man: at this rate your work will be that

post.

So, the other day, you appended to your signature, as it were, though

it's not the four lines nor is it split from the body with --, that

there was such a linear mapping, then, how is [0,1] or the CIBT or

Cantor space of the Cantor set of the sequences 2^w, a linear space?

It's simple to define operations that would be fields except for

associativity of *, distributivity, or multiplicative inverses, so I

wonder what positive input you had in mind (and that they would

otherwise satsify the vector space axioms). A simple and trivial

continuous mapping was noted.

Regards,

Ross Finlayson