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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 4:38 PM

On 8 Mrz., 22:19, quasi <qu...@null.set> wrote:
> netzweltler wrote:
> >quasi wrote:
>
> >> 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?
>
> I don't understand the mechanics or the intent of the above
> marking scheme.
>
> But I think you've fallen victim to a common fallacy.
>
> When trying to determine whether or not an infinite set is
> countable, a failed counting _doesn't_ disprove countability.

I am not trying to prove or disprove countability of these segments in
[0, 1]. Remember, we have been discussing if the choice of #1 (or #0
as you suggested) is arbitrary. Let me give the answer to my question
instead: All segments in [0, 1] have been marked #0 at t = 1 s. So,
there are no segments left to be marked #-1, #-2, ..., are there?

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