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

 Messages: [ Previous | Next ]
 quasi Posts: 12,067 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 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.

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