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

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 Frederick Williams Posts: 2,164 Registered: 10/4/10
Re: Cardinality of turning wheel
Posted: Mar 7, 2013 12:08 PM

Don Kuenz wrote:
>
> Shmuel (Seymour J.) Metz <spamtrap@library.lspace.org.invalid> wrote:

> > In <20130302a@crcomp.net>, on 03/02/2013
> > at 08:28 PM, Don Kuenz <garbage@crcomp.net> said:
> >

> >>If we can somehow use sin(x) to represent the number of revolutions,
> >
> > What does that mean? That function has the range [-1,1].
> >

> >>where [x] is the rational part of x.
> >
> > What does that mean? There is no "rational part" of an irrational
> > number.

>
> The physics forum to argue:
> a. create a subset r containing only the rationals from R
> b. the cardinality of R is c and the cardinality of sin(x) is c
> c. therefore, the cardinality of sin(r) is c * c

Again: it is sets that have a cardinality. What set is sin(x)? The
range of sin (with domain R) is [-1,1] which has cardinality c. The
graph of sin is a subset of R^2, the cardinality of R^2 is c*c = c. The
set of rationals has cardinality aleph_0. If you are taking the domain
of sin to be the set of rationals then see my post of Thu, 07 Mar 2013
17:03:22 +0000.

--
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

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
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3/3/13 netzweltler
3/3/13 Brian Chandler
3/4/13 netzweltler
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3/3/13 Frederick Williams
3/3/13 quasi
3/4/13 netzweltler
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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