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Re: Matheology § 062
Posted:
Jul 8, 2012 6:28 AM
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On 8 Jul., 06:54, William Hughes <wpihug...@gmail.com> wrote:
> On Jul 7, 12:15 pm, "LudovicoVan" <ju...@diegidio.name> wrote:
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> > "WM" <mueck...@rz.fh-augsburg.de> wrote in message
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> >news:6ed4b3b7-14a1-42ba-beb6-c0fe3a1cfd1c@5g2000vbf.googlegroups.com...
> > <snip>
>
> > > After 1 hour the urn is empty, because for every number the time of
> > > removal can be determined. So for the set X of numbers residing in the
> > > urn we obtain
> > > Lim |X| =/= |Lim X|
> > > This prevents any application of set theory to reality although it was
> > > Cantor's outspoken aim to apply set theory to reality (cp., e.g., his
> > > letter to Mittag-Leffler of Sept., 22, 1884).
>
> > That argument is simply *wrong*, it does not show a problem in set theory
> > (not in itself at least). From "every (finitely-labeled!) ball has been
> > removed at step w" one cannot conclude "the vase is empty at step w",
> > period.
>
> > -LV
>
> One can certainly conclude that the vase does not
> contain any finitely-labeled balls. If we define
> |X| to be the number of finitely-labeled balls
> then WM's conclusion follows.-
But only in set theory - not in mathematics.
Because in mathematics the limit of the sequence
21
2.1
432.1
43.21
6543.21
654.321
...
is not 0 but oo.
http://www.hs-augsburg.de/~mueckenh/GU/GU12c.PPT#403,25,Folie 25
Regards, WM
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