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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 18, 2009 7:22 AM

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.

> So the notion of n
> growing bigger, as one tends to the limit, is not embodied
> here since |n| is 0,1,1,1,1... as one proceeds and is 0 in
> the limiting case.

Yes, as in many cases: lim | S_n | is not necessarily equal to |lim S_n|,
whatever the definition of set limit. The same holds for limsup and
liminf.
--
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