Date: Mar 7, 2013 3:37 PM
Author: quasi
Subject: Re: Cardinality of turning wheel
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.

quasi