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Topic: Cardinality of turning wheel
Replies: 43   Last Post: Mar 10, 2013 1:55 AM

 Messages: [ Previous | Next ]
 netzweltler Posts: 473 From: Germany Registered: 8/6/10
Re: Cardinality of turning wheel
Posted: Mar 8, 2013 3:43 PM

On 7 Mrz., 21:37, quasi <qu...@null.set> wrote:
> netzweltler wrote:
> >quasi wrote:
> >> netzweltler wrote:
> >> >quasi wrote:
>
> >> >>As far as the notion of infinite speed, I see the
> >> >>specification of such a model as problematic, but as I
> >> >>said, I would be willing to look at a proposal for such
> >> >>a model, so long as the assumptions were fully specified,
> >> >>and sufficient justification for analyzing the model was
> >> >>provided.

>
> >> >Is the notion of infinite speed more problematic to you
> >> >than the notion, that any revolution of the countably
> >> >infinite set of revolutions can be the origin -
> >> >revolution #1?

>
> >> No, the choice of origin is arbitrary.
>
> >There are countably infinitely many segments [0, 0.5] (#1),
> >[0.5,0.75] (#2), [0.75, 0.875] (#3), ... in [0, 1].

>
> >If the choice of #1 is arbitrary I can name any of these
> >segments #1. If any segment of size > 0 can be #1, which
> >segments are left to mark #2, #3, and so on?

>
> Mark them with non-positive integers, #0, #-1, #-2, ...
>
> Any infinite set of pairwise disjoint intervals on the real
> line is countably infinite since each interval contains a
> distinct rational number.

t = 0 s: I am marking [0, 0.5] #0, [0.5, 0.75] #-1, [0.75, 0.875]
#-2, ...
t = 0.5 s: I am marking [0.5, 0.75] #0, [0.75, 0.875] #-1, [0.875,
0.9375] #-2, ...
t = 0.75 s: I am marking [0.75, 0.875] #0, [0.875, 0.9375] #-1,
[0.9375, 0.96875] #-2, ...
...

Which segments have been marked #0 after 1 s?

Date Subject Author
3/2/13 netzweltler
3/2/13 Frederick Williams
3/2/13 quasi
3/2/13 netzweltler
3/2/13 William Elliot
3/3/13 quasi
3/3/13 netzweltler
3/3/13 quasi
3/3/13 netzweltler
3/3/13 quasi
3/3/13 netzweltler
3/3/13 Brian Chandler
3/4/13 netzweltler
3/3/13 quasi
3/3/13 Frederick Williams
3/3/13 quasi
3/4/13 netzweltler
3/4/13 quasi
3/4/13 Shmuel (Seymour J.) Metz
3/5/13 Frederick Williams
3/5/13 netzweltler
3/5/13 quasi
3/6/13 netzweltler
3/6/13 quasi
3/7/13 netzweltler
3/7/13 quasi
3/8/13 netzweltler
3/8/13 quasi
3/8/13 netzweltler
3/8/13 quasi
3/8/13 Frederick Williams
3/2/13 Frederick Williams
3/3/13 Frederick Williams
3/5/13 K_h
3/7/13 Frederick Williams
3/7/13 Frederick Williams
3/3/13 Shmuel (Seymour J.) Metz
3/7/13 Frederick Williams
3/10/13 Shmuel (Seymour J.) Metz