
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

