netzweltler
Posts:
337
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?

