Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: cbrown@xxxxxxxxxxxxxxxxx
- Date: Tue, 12 Feb 2008 09:15:12 -0800 (PST)
On Feb 12, 5:58 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
Gonçalo Rodrigues wrote:
Is that your pavlovian response whenever you see some mathematics that
is beyond your understanding? That it is an unnecessary complication?
Geez! In my _finitary_ comprehension, the whole thing is sooo obvious !
But that's not the game I want to play here. Therefore I'm _begging_ you
to employ a formalism which is as simple and straghtforward as possible
and not invoke unneccessary complications / generalizations or whatever.
It's quite simple and natural: according to the proposed definitions,
given a sequence of sets (A_1, A_2, ..., A_n, ...) we say that
If there is an n such that element a is never in /any/ A_m for m > n,
then a must /not/ be in the limit set.
If there is an n such that element a is always in /every/ A_m for m >
n, then a must be in the limit set.
If there are elements a such that neither of the above two cases hold,
then the limit set is not well-defined.
Example application:
If you remove a ball from the vase at time t before noon, and at no
time t1 > t do you return the ball to the vase, then the ball is not
in the vase at noon.
If you put a ball in the vase at time t before noon, and at no time t1
t do you remove it, then the ball is still in the vase at noon.
If neither of the above cases hold for a particular ball, then "the
ball is in the vase at noon" is undefined for that ball; and therefore
"the set of balls in the vase at noon" is undefined.
Cheers - Chas
.
- References:
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: G . Frege
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Han . deBruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Jesse F. Hughes
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Han de Bruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Jesse F. Hughes
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Gonçalo Rodrigues
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Han de Bruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: G . Frege
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Jesse F. Hughes
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Han de Bruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Gonçalo Rodrigues
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Han de Bruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
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