netzweltler
Posts:
278
From:
Germany
Registered:
8/6/10
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Re: Cardinality of turning wheel
Posted:
Mar 3, 2013 5:28 AM
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On 3 Mrz., 11:04, quasi <qu...@null.set> wrote:
> netzweltler wrote:
> >quasi 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?"
>
> As I see it, revolutions correspond to time points on the number
> line.
>
> The concept of perpetual revolution without beginning or end
> implies that for each revolution, there is a previous one and a
> next one. Hence if two consecutive revolutions occur at times
> t1 and t2 with t1 < t2, the average rotational velocity for the
> time interval [t1,t2] is 1/(t2-t1) revolutions per unit time.
>
> So yes, the concepts of time and velocity are relevant.
Is it true to say, that the cardinality of the set of revolutions of
the wheel depends on the velocity? So, can be aleph_0 or aleph_1? See
this post:
On 3 Mrz., 03:17, William Elliot <ma...@panix.com> wrote:
> On Sat, 2 Mar 2013, netzweltler wrote:
> > On 2 Mrz., 20:39, quasi <qu...@null.set> wrote:
>
> > > 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?
>
> No. In that case the wheel, necessarily composed of purely virtual
> fantasy, would have spun, in it's eternal life, aleph_1 times.
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