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 ]
 William Elliot Posts: 2,637 Registered: 1/8/12
Re: Cardinality of turning wheel
Posted: Mar 2, 2013 9:17 PM

On Sat, 2 Mar 2013, netzweltler wrote:
> On 2 Mrz., 20:39, quasi <qu...@null.set> 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?

No. In that case the wheel, necessarily composed of purely virtual
fantasy, would have spun, in it's eternal life, aleph_1 times.

Riddle of the day. How long is eternity?
aleph_0 years, aleph_1 days, aleph_2 seconds?

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