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Topic: Matheology § 074
Replies: 114   Last Post: Jul 22, 2012 4:15 PM

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: Matheology § 074
Posted: Jul 15, 2012 11:42 AM
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On 15 Jul., 16:49, "LudovicoVan" <ju...@diegidio.name> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> wrote in message

> > If the definitions of set theory are applied, then they are both
> > empty. (For instance, there is no natural number that is always in the
> > set M_n.)

>
> I have checked those definitions again.  There are surely details still
> above my head, yet everything seems to sum up quite well: the two limits
> just diverge.


No. They are both empty:
After the k-th step there have been 2k numbers introduced and are k
numbers removed, so that
M_k = {k+1, k+2, k+3, ..., 2k}

LimSup (M_n) = /\(n = 1 ... oo)[\/(k = n ... oo) M_k]

\/(k = n ... oo) M_k = {n+1, n+2, n+3, ...}
/\(n = 1 ... oo)[\/(k = n ... oo) M_k] =
{2, 3, 4, ...} /\ {3, 4, 5, ...} /\ ... /\ {n+1, n+2, n+3, ...} /\ ...
= { }

LimInf (M_n) = \/(n = 1 ... oo)[/\(k = n ... oo) M_k]
/\(k = n ... oo) M_k = {n+1, n+2, n+3, ...} /\
{n+1+1, n+1+2, n+1+3, ...} /\ ... = { }
\/(n = 1 ... oo)[/\(k = n ... oo) M_k] =
{ } \/ { } \/ { } \/ ... = { }

Regards, WM


Date Subject Author
7/13/12
Read Matheology § 074
mueckenh@rz.fh-augsburg.de
7/13/12
Read Re: Matheology § 074
MoeBlee
7/13/12
Read Re: Matheology � 074
Virgil
7/14/12
Read Re: Matheology § 074
dilettante
7/14/12
Read Re: Matheology § 074
LudovicoVan
7/14/12
Read Re: Matheology § 074
dilettante
7/14/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/14/12
Read Re: Matheology § 074
LudovicoVan
7/14/12
Read Re: Matheology � 074
Virgil
7/14/12
Read Re: Matheology § 074
dilettante
7/14/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/14/12
Read Re: Matheology § 074
dilettante
7/14/12
Read Re: Matheology § 074
LudovicoVan
7/14/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/15/12
Read Re: Matheology § 074
LudovicoVan
7/15/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/15/12
Read Re: Matheology § 074
LudovicoVan
7/15/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology § 074
LudovicoVan
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology � 074
Virgil
7/14/12
Read Re: Matheology � 074
Virgil
7/14/12
Read Re: Matheology § 074
dilettante
7/15/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/15/12
Read Re: Matheology § 074
dilettante
7/15/12
Read Re: Matheology § 074
Frederick Williams
7/15/12
Read Re: Matheology § 074
dilettante
7/15/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/15/12
Read Re: Matheology § 074
dilettante
7/16/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/16/12
Read Re: Matheology § 074
LudovicoVan
7/16/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/16/12
Read Re: Matheology § 074
LudovicoVan
7/17/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/17/12
Read Re: Matheology � 074
Virgil
7/16/12
Read Re: Matheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology § 074
LudovicoVan
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology § 074
LudovicoVan
7/16/12
Read Re: WM's WMatheology § 074
LudovicoVan
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/17/12
Read Re: WM's WMatheology § 074
William Hughes
7/18/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/18/12
Read Re: WM's WMatheology § 074
LudovicoVan
7/18/12
Read Re: WM's WMatheology § 074
LudovicoVan
7/18/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/18/12
Read Re: WM's WMatheology § 074
LudovicoVan
7/18/12
Read Re: WM's WMatheology � 074
Virgil
7/18/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/18/12
Read Re: WM's WMatheology � 074
Virgil
7/19/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/19/12
Read Re: WM's WMatheology � 074
Virgil
7/18/12
Read Re: WM's WMatheology � 074
Virgil
7/18/12
Read Re: WM's WMatheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology § 074
LudovicoVan
7/16/12
Read Re: WM's WMatheology § 074
MoeBlee
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/16/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/16/12
Read Re: WM's WMatheology � 074
Virgil
7/17/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/17/12
Read Re: WM's WMatheology � 074
Virgil
7/17/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/17/12
Read Re: WM's WMatheology � 074
Virgil
7/18/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/18/12
Read Re: WM's WMatheology � 074
Virgil
7/18/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/18/12
Read Re: WM's WMatheology � 074
Virgil
7/19/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/19/12
Read Re: WM's WMatheology � 074
Virgil
7/19/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/19/12
Read Re: WM's WMatheology � 074
Virgil
7/19/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/19/12
Read Re: WM's WMatheology § 074
YBM
7/19/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/19/12
Read Re: WM's WMatheology � 074
Virgil
7/19/12
Read Re: WM's WMatheology § 074
FredJeffries@gmail.com
7/19/12
Read Re: WM's WMatheology § 074
MoeBlee
7/19/12
Read Re: WM's WMatheology � 074
Virgil
7/19/12
Read Re: WM's WMatheology § 074
MoeBlee
7/20/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/20/12
Read Re: WM's WMatheology � 074
Virgil
7/20/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/20/12
Read Re: WM's WMatheology � 074
Virgil
7/20/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/20/12
Read Re: WM's WMatheology � 074
Virgil
7/21/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/21/12
Read Re: WM's WMatheology � 074
Virgil
7/22/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/22/12
Read Re: WM's WMatheology � 074
Virgil
7/20/12
Read Re: WM's WMatheology § 074
Marshall
7/20/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/20/12
Read Re: WM's WMatheology § 074
YBM
7/20/12
Read Re: WM's WMatheology � 074
Virgil
7/21/12
Read Re: WM's WMatheology § 074
mueckenh@rz.fh-augsburg.de
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology � 074
Virgil
7/15/12
Read Re: Matheology � 074
Virgil
7/14/12
Read Re: Matheology § 074
mueckenh@rz.fh-augsburg.de
7/14/12
Read Re: Matheology § 074
dilettante
7/14/12
Read Re: Matheology § 074
LudovicoVan
7/14/12
Read Re: Matheology � 074
Virgil
7/14/12
Read Re: Matheology � 074
Virgil

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