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Topic: Matheology § 285
Replies: 84   Last Post: Jun 15, 2013 6:05 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 285
Posted: Jun 13, 2013 7:50 PM
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In article <d6367536-0d82-41c3-a4b4-2d6f576dc485@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> On Wednesday, 12 June 2013 22:59:24 UTC+2, Zeit Geist wrote:
>
>

> > > > Every finite one can, but not the entire set of Q.
>
> > > I prove that all elements of Q can be well-ordered by size. You cannot
> > > disprove it, because you cannot find any element that stays outside, can
> > > you?

> >
> >
> >
> > You proved nothing!

>
> Your nded unfouopinion is not of interest in this connection.


But WM's opinion is provably of immensely negative value on this and
most other mathematical issues.
> >
> > You proposed an algorithm,
> >
> > But never showed that it conclusively does what you say.

>
> You can take whatever algorith you like to well-order by size any finite set
> of rationals.



And it will fail to well-order any subset of the rationals that is not
normally well-ordered.

A FINITE union of well ordered-sets with compatible orderings will also
be well-ordered.

An INFINITE union of well-ordered sets with compatible orderings need
not be well-ordered.

Since infinite unions, like other infiniteness, is exiled from the wild
weird world of WMytheology, the set of rationals in WMytheology, being
necessarily finite in WMytheology, may well be well-ordered to begin
with, but outside WMytheology, it is not and cannot be made so by WM's
wand waving.

The set of rationals with its standard ordering is never well-ordered
outside the wild weird world of WMytheology, no matter what WM tries to
do to it.

WM's false claim is that an INFINITE union of compatibly ordered
well-ordered sets must be well-ordered. It is this provably false
assumption on which WM's provably false argument depends.

WM claims that unioning any sequence of well-ordered sets
, for example, {-1}, {-2,-1}, {-3, -2, -1}, ...
will force the resulting infinite union, such as {...,-3, -2, -1}, to be
well-ordered (i.e., every non-empty subset of {...,-3, -2, -1} including
{...,-3, -2, -1} itself has, at least according to WM's claim, a most
negative member).

To repeat, WM claims that every non-empty subset of {...,-3, -2, -1},
including the set itself, must have a first/most-negative member.

I challenge WM to provide us with any first/most-negative member of that
set of all negative integers.

Or, for that matter, of any of its supersets, including Q.





> Since every rational number q_i belongs to a finite set of i
> rationals, this proves that all rationals can be ordered by size -


Only in the wild weird world of WMytheology, where the set of rationals
is finite.
> > >
> >
> > > > Any finite set of real numbers can be well- according to magnitude.
> > > > Infinite ones, not necessarily.

>
> I stated that all rationals that belong to FIS of the enumeration can be
> well-ordered by size.


Which may well be the case WITHIN the wild weird world of WMytheology,
where all sets are finite, since l finite ordered sets are all
automatically well-ordered, but is not true anywhere that allows the
rationals to be densely ordered.
> >
>
> > >
> >
> > > Either find a q that stays outside of the well-order by size. If such a q
> > > exists and is enumerated as q_n, then there is a first natural number n
> > > that cannot be put in a permutation such that all q's are in order by
> > > size. If such a q exists and cannot be enumerated, then countability is
> > > nonsense.

>
> > Sure thing.
> >
> > If the enumeration has f(j) = 1/2,
> >
> > what is f(j+1), f(j+2) and f(j+3)?

>
> That depends on the enumeration you choose at the outset. Take Cantor's
> original one.

> >
> >
> >
> > If f keeps the order we must have
> >
> >
> >
> > | f(m) | <= | f(m+1) |

>
> f does not keep the order. Always when you extend the set of rationals, you
> order them by size. This is possible for every finite set, i.e., for every
> FIS of the enumerated set.

> >
> >
> >
> > And no rational r, such that the magnitude
> >
> > Of r is in between that of f(m) and f(m+1).

>
> You are lacking understanding.
>
> Take the first i rationals, order them by size. Add the rational with number
> i+1put them in the correct order by size with the others. And so on without
> ever arriving at an infinite i and without leaving out any rational q_i or
> q_i+1 or any desired rational.


When inside WMs wild weird world of WMytheology, where all sets are
finite, all ordered sets are also well-ordered, but as soon as any
infinite ordered sets are allowed, WM's arguments fail.
--




Date Subject Author
6/11/13
Read Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
JT
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
Ralf Bader
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/14/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/14/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/15/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/15/13
Read Re: Matheology � 285
Virgil
6/15/13
Read Re: Matheology � 285
Tanu R.
6/15/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 285
Virgil
6/15/13
Read Re: Matheology � 285
Virgil
6/14/13
Read Re: Matheology � 285
Virgil
6/13/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology � 285
Virgil
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: WMytheology ???
Virgil
6/12/13
Read Re: WMytheology ???
Scott Berg
6/12/13
Read Re: WMytheology ???
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology § 285
Virgil
6/12/13
Read Re: Matheology § 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
LudovicoVan
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology § 285
LudovicoVan
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re:Outside the wild weird world of WMytheology
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology � 285
Virgil
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
LudovicoVan
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology � 285
Tanu R.
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology � 285
Tanu R.
6/11/13
Read Re: Matheology ? 285
Virgil
6/11/13
Read Re: Matheology ? 285
Tanu R.

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