Don Kuenz wrote: > > netzweltler <firstname.lastname@example.org> 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