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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 14, 2009 7:57 PM

"Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
news:KunEFz.913@cwi.nl...
> In article <k9mdnWn11pFIAbjWnZ2dnUVZ_uWdnZ2d@giganews.com>
> "K_h" <KHolmes@SX729.com> writes:

> > "Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message
> > news:878wd7lczh.fsf@phiwumbda.org...

> ...
> > >> The basic idea of what a limit is suggests that an
> > >> appropriate definition for lim(n-->oo){n} should
> > >> yield
> > >> lim(n-->oo){n}={N}:
> > >>
> > >> {0}, {{0}}, {{0,1}}, {{0,1,2}}, {{0,1,2,3}}, ...-->
> > >> {{0,1,2,3,4,...}}

>
> Why?

Why not?

> (And the first should be {{}}.)

Yes, my mistake; corrected above.

> > 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.

>
> It is not.

Why not?

> >
> > Otherwise
> > let L=lim(n-->oo)X_n be the specified wikipedia limit
> > for
> > X_n. If L exists then:

>
> So you wish to use different definitions of limits
> depending on what
> the sequence of sets actually is?

No, the defintion I provided is one defintion that includes
stuff from the wikipedia definition.

> > 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} and
> > |lim(n-->oo){n}|=lim(n-->oo)|{n}|=1. Even this
> > definition
> > can be improved. In the spirit of what a good
> > definition of
> > a limit should be, we should require that, for example,
> > lim(n-->oo){n,n,n}={N,N,N}.

>
> Eh? This is not a limit of sets but a limit of multisets.

Good point.

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