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

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K_h

Posts: 419
Registered: 4/12/07
Re: Another AC anomaly?
Posted: Dec 18, 2009 3:39 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


"K_h" <KHolmes@SX729.com> wrote in message
news:SqSdnSUF1q8FobbWnZ2dnUVZ_uCdnZ2d@giganews.com...
>
> "Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
> news:Kusoty.176@cwi.nl...

>> In article
>> <yrydnX_FwfczULTWnZ2dnUVZ_vmdnZ2d@giganews.com> "K_h"
>> <KHolmes@SX729.com> writes:
>> ...

>> > lim(n ->oo) n = N is true for the standard definition
>> > of
>> > natural numbers using just the wikipedia definitions
>> > for the
>> > limit of a sequence of sets.

>>
>> But not with Zermelo's definition of the natural numbers.
>> Nor when we take
>> the natural numbers as embedded in the rational numbers.

>
> Yes, and that was never denied. I just point out that any
> limit definition for a sequence of sets will give answers
> that violate the intuitive notion of a limit for certain
> constructions. There are two ways one can deal with that.
> First, for a given class of constructions, have another
> definition that does not violate the limit notion. The
> second way is to look at the meaning that the wikipedia
> definitions have for the constructions. I now think that
> the latter approach is superior to the first since the
> first caused so much misunderstanding. 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. What this means is
> that nothing is `accumulated' in a limit set since each
> set does not persist past its introduction. 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. Under the standard
> construction each natural is `accumulated' in the limit
> set, since each set persists beyond its introduction, and
> this preserves the notion of n growing bigger as one
> proceeds: |n| is 0,1,2,3,... and is N in the limiting
> case.


Yo, it should be |N| in the limiting case!

k




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

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