netzweltler
Posts:
425
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 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.
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?

