quasi
Posts:
9,080
Registered:
7/15/05
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Re: Cardinality of turning wheel
Posted:
Mar 7, 2013 3:37 PM
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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
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