quasi
Posts:
10,561
Registered:
7/15/05


Re: Cardinality of turning wheel
Posted:
Mar 7, 2013 3:37 PM


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 nonpositive 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

