quasi
Posts:
9,078
Registered:
7/15/05
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Re: Cardinality of turning wheel
Posted:
Mar 3, 2013 1:05 AM
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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
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