Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Cardinality of turning wheel
Replies: 43   Last Post: Mar 10, 2013 1:55 AM

 Messages: [ Previous | Next ]
 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 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

Date Subject Author
3/2/13 netzweltler
3/2/13 Frederick Williams
3/2/13 quasi
3/2/13 netzweltler
3/2/13 William Elliot
3/3/13 quasi
3/3/13 netzweltler
3/3/13 quasi
3/3/13 netzweltler
3/3/13 quasi
3/3/13 netzweltler
3/3/13 Brian Chandler
3/4/13 netzweltler
3/3/13 quasi
3/3/13 Frederick Williams
3/3/13 quasi
3/4/13 netzweltler
3/4/13 quasi
3/4/13 Shmuel (Seymour J.) Metz
3/5/13 Frederick Williams
3/5/13 netzweltler
3/5/13 quasi
3/6/13 netzweltler
3/6/13 quasi
3/7/13 netzweltler
3/7/13 quasi
3/8/13 netzweltler
3/8/13 quasi
3/8/13 netzweltler
3/8/13 quasi
3/8/13 Frederick Williams
3/2/13 Frederick Williams
3/3/13 Frederick Williams
3/5/13 K_h
3/7/13 Frederick Williams
3/7/13 Frederick Williams
3/3/13 Shmuel (Seymour J.) Metz
3/7/13 Frederick Williams
3/10/13 Shmuel (Seymour J.) Metz