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Topic: Another AC anomaly?
Replies: 43   Last Post: Dec 21, 2009 8:08 AM

 Messages: [ Previous | Next ]
 Dik T. Winter Posts: 7,899 Registered: 12/6/04
Re: Another AC anomaly?
Posted: Dec 15, 2009 9:53 PM

In article <Kup2uH.JC7@cwi.nl> "Dik T. Winter" <Dik.Winter@cwi.nl> writes:
> In article <r_6dnUXDv4pMfbvWnZ2dnUVZ_tWdnZ2d@giganews.com> "K_h" <KHolmes@SX729.com> writes:
> > "Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
> > news:KunF0v.9y9@cwi.nl...

> ...
> > > By what definition is:
> > > lim(n -> oo) n = N?

> >
> > Any of the wikipedia definitions. Here is the proof again.

> ...
> > Theorem:
> > lim(n ->oo) n = N. Consider the naturals:
> >
> > S_0 = 0 = {}
> > S_1 = 1 = {0}

> ...
> This presupposes a particular construction for the natural number. There are
> other constructions that are consistent with ZF. Is the limit valid for all
> those possible models?

For starters, try it with
0 = {}
n+1 = {n}
which is a valid construction of the naturals in ZF.

Even with your definition
lim sup(n -> oo) {n} = {}
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

Date Subject Author
12/12/09 Jesse F. Hughes
12/13/09 K_h
12/14/09 Dik T. Winter
12/14/09 K_h
12/15/09 Dik T. Winter
12/15/09 K_h
12/16/09 Dik T. Winter
12/16/09 K_h
12/17/09 Dik T. Winter
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/21/09 Dik T. Winter
12/14/09 Dik T. Winter
12/14/09 K_h
12/15/09 Dik T. Winter
12/15/09 Dik T. Winter
12/15/09 K_h
12/16/09 Dik T. Winter
12/17/09 K_h
12/17/09 Dik T. Winter
12/18/09 K_h
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/15/09 K_h
12/16/09 Jesse F. Hughes
12/17/09 Dik T. Winter
12/17/09 Jesse F. Hughes
12/16/09 Dik T. Winter
12/15/09 ross.finlayson@gmail.com
12/13/09 K_h
12/13/09 Jesse F. Hughes
12/13/09 Jesse F. Hughes
12/14/09 Ilmari Karonen
12/14/09 Jesse F. Hughes
12/15/09 Chas Brown