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

 Messages: [ Previous | Next ]
 K_h Posts: 419 Registered: 4/12/07
Re: Another AC anomaly?
Posted: Dec 18, 2009 8:10 PM

"Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
news:KuuL11.56J@cwi.nl...
> In article <SqSdnSUF1q8FobbWnZ2dnUVZ_uCdnZ2d@giganews.com>
> "K_h" <KHolmes@SX729.com> writes:
> ...

> > With the second option
> > we
> > can restrict ourselves just to the wikipedia definitions
> > and
> > define the sets n by:
> >
> > n = 0 = {}
> > n = 1 = {{}}
> > n = 2 = {{{}}}
> > ...
> >
> > Wikipedia gives liminf(n-->oo) n = 0.

>
> Only when we use the definition of limit on sequences of
> sets, not when we
> use the definition of limit on sequences of numbers. You
> have to distinguish
> the two and clearly state which one you are using.

In ZF set theory numbers are defined by sets and in this
case there is no difference:

0 = {}
1 = {{}}
2 = {{{}}}
...

If the natural numbers are defined by these sets then
liminf(n-->oo)n=0. But yes, on the real number line, the
"naturals" are still defined by sets but limits on real
numbers are not defined by limits on their associated sets.

k

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