netzweltler
Posts:
473
From:
Germany
Registered:
8/6/10


Re: Cardinality of turning wheel
Posted:
Mar 3, 2013 4:38 AM


On 3 Mrz., 07:05, quasi <qu...@null.set> wrote: > netzweltler wrote: > >quasi wrote: > >> netzweltler wrote: > >> >What is the cardinality of the number of revolutions of a > >> >turning wheel, if there is no beginning and no end to it? > > >> For a wheel revolving forever (both past and future), the > >> set of revolutions is in onetoone correspondence with the > >> set of integers, hence has cardinality aleph0. > > >Is this still true, if the wheel is revolving at infinite > >speed, meaning, that we can see at least one revolution no > >matter how small the time we are watching it? > > That's totally inconsistent with my intuition about velocity > and time.
Do we need to define 'velocity' and 'time'? Do we need to assign an origin, past and future to give a valid answer to the question "What is the cardinality of the number of revolutions of a turning wheel, if there is no beginning and no end to it?"
> I assumed that instants of time could be represented > onetoone as points on the real number line, and that there > exist real numbers a,b with 0 < a <= b such that at any > instant of time, the velocity v of the wheel, expressed in > revolutions per unit time, is between a and b inclusive. > > quasi

