|
|
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
|
|
