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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 14, 2009 10:29 AM

In article <k9mdnWn11pFIAbjWnZ2dnUVZ_uWdnZ2d@giganews.com> "K_h" <KHolmes@SX729.com> writes:

Let's see whether I do understand what you want:
...
> The sensibility of a definition is the real issue. Applying
> the so-called standard definitions to {n} leads to a
> cockamamie limit which is at odds with the general notion of
> a limit.

> For a better definition, first choose one of the
> wikipedia definitions.

We better choose a definition that fits, let's take the definition for
sets with discrete metric on the elements.

> If a sequence of sets, A_n, cannot
> be expressed as {X_n}, for some sequence of sets X_n, then
> lim(n-->oo)A_n is defined by the wikipedia limit.

So with that definition lim sup(n -> oo) {1/n} = {} (note: we use
a discrete metric on the rational numbers).

> Otherwise
> let L=lim(n-->oo)X_n be the specified wikipedia limit for
> X_n. If L exists then:
>
> lim(n-->oo)A_n = lim(n-->oo){X_n} = {L}
>
> otherwise lim(n-->oo)A_n = lim(n-->oo){X_n} does not exist.
> Under this definition lim(n-->oo){n}={N}

By what definition is it {N}? By what definition is:
lim(n -> oo) n = 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