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Re: Cardinality of turning wheel
Posted:
Mar 3, 2013 10:32 AM
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Don Kuenz wrote:
>
> netzweltler <reinhard_fischer@arcor.de> wrote:
> > What is the cardinality of the number of revolutions of a turning
> > wheel, if there is no beginning and no end to it?
>
> If we can somehow use sin(x) to represent the number of revolutions,
> here's an argument that the cardinality of sin(x) is c^c.
It is sets that have a cardinality. What set is sin(x)?
> http://www.physicsforums.com/showpost.php?p=1987697
>
> Given A a subset of R... we can map [0,1) onto R, so we
> can map [0,1) onto A, say by a function f. Then extend
> f to a function F by F(x) = f([x]) where [x] is the
> rational part of x. F is periodic and has as its range
> A. Hence for each subset of R, we have a distinct
> periodic function, and then just use the fact that the
> set of periodic functions is a subset of the set of all
> functions R->R and the cardinality of the latter is c^c
>
> Unfortunately a) cardinalities are new to me, and b) how to map the
> *number* of revolutions into sin(x) eludes me.
>
> --
> Don Kuenz
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
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