"Frederick Williams" wrote in message news:51336CFB.CDE15F2C@btinternet.com... > > > 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)?
Don put forward a bad argument. The sine function is the set of all points (x, sin(x)) where x is any real number. So the cardinality of sin(x) is just c, the cardinality of the real line because there are two values in (x, sin(x)) and 2*c=c in cardinal arithmetic.