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Topic: Matheology § 223: AC and AMS
Replies: 102   Last Post: Apr 18, 2013 12:26 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 223: AC and AMS
Posted: Mar 14, 2013 3:58 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 14 Mrz., 13:59, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
> > > On 14 Mrz., 12:35, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> > >> WM <mueck...@rz.fh-augsburg.de> writes:
> > >> > According to standard matheology one can choose one element each of an
> > >> > uncountable set of sets. That is as wrong. Compare Matheology § 225.

Only in WM's corrupted version of math is anyone ever forced to use the
axiom of choice, though there is little reason to object to it.
> >
> > >> You can and do of course  reject this axiom.
> >
> > >> To show something is self-contradictory, however, you need to use the
> > >> reasoning principles of the system you want to show is

> >
> > > The axiom belongs to the system. It says that elements can be chosen.

The AOC is NOT a required part of THE system, but is entirely optional,
and there is not much important mathematics that cannot be done, though
with much greater difficulty, without it.

> > > To choose immaterial elements,  hmm, how is that accomplished in a
> > > system that contains the axiom of choice?

One always chooses material elements.
> >
> > I can only repeat myself --
> > where is the *logical* contradiction there, in terms of classical
> > mathematics?

>
> You will find it if you try to answer my question. Choosing means
> defining (by a finite number of words) a chosen element (unless it is
> a material object). No other possibility exists.

> >
> > Of course, you think it's false, and unimaginable, and whatever
> > words you want to use.
> >
> > But you claim it's *self-contradictory*, don't you?
> >
> > And that's a whole different claim.

>
> Please look up what Zermelo wrote. (In Matheology § 225 you will find
> the orginal German text.) It is always possible /to choose/ an element
> from every non-empty set and to union the chosen elements into a set
> S_1.

If that is what Zermelo said then he was wrong to say it because one
does not ever "union" elements, only sets.
>
> This means: It is possible to have and to apply uncountably many
> finite words in order to choose and in order to distinguish the
> elements in S_1 (a set can have only distinct elements by axiom).

What axiom says that a set can only have "distinct" elements, and what
does it mean for elements to be "distinct"?
Certainly in the real line, the elements form a continuum, in which they
are NOT distinct in any usual sense as there is never a next larger or
next smaller real.

***********************************************************************

WM has frequently claimed that a 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 must first
show that the set of all binary sequences is a vector space and that the
set of paths of a CIBT is also a vector space, which he has not done and
apparently cannot do, and then show that his mapping satisfies the
linearity requirement that
f(ax + by) = af(x) + bf(y),
where a and b are arbitrary members of a field of scalars and x and y
are f(x) and f(y) are vectors in suitable linear spaces.

By the way, WM, what are a, b, ax, by and ax+by when x and y are binary
sequences?

If a = 1/3 and x is binary sequence, what is ax ?
and if f(x) is a path in a CIBT, what is af(x)?

Until these and a few other issues are settled, WM will still have
failed to justify his claim of a LINEAR mapping from the set (but not
yet proved to be vector space) of binary sequences to the set (but not
yet proved to be vector space) of paths ln a CIBT.

Just another of WM's many wild claims of what goes on in his WMytheology
that he cannot back up.
--

Date Subject Author
3/14/13 Alan Smaill
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 Virgil
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
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3/19/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
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3/19/13 Virgil
3/19/13 fom
3/19/13 Virgil
3/19/13 Virgil
4/17/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
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3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
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3/18/13 Virgil
3/18/13 fom
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3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
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3/19/13 Virgil
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4/17/13 Virgil
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3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 Virgil
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3/16/13 Virgil
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3/15/13 fom
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3/15/13 Virgil
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3/16/13 Virgil
3/14/13 Virgil
3/14/13 Virgil
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3/16/13 Virgil
3/17/13 fom