netzweltler
Posts:
278
From:
Germany
Registered:
8/6/10
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Re: Cardinality of turning wheel
Posted:
Mar 3, 2013 4:38 AM
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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 one-to-one correspondence with the
> >> set of integers, hence has cardinality aleph-0.
>
> >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
> one-to-one 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
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