quasi
Posts:
10,226
Registered:
7/15/05


Re: Cardinality of turning wheel
Posted:
Mar 3, 2013 1:05 AM


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.
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

