01/04/2008, 06:51 PM

jaydfox Wrote:infinitesimals would necessarily have density measured with 2^CIf this is true, then there cannot be an isomorphism between the standard field of complex numbers where i is imaginary unit (Cardinality of the reals), and the non-standard field of where z is an infinitesimal (Cardinality of the powerset of reals), as Ivars suggests. If they are of fundamentally different cardinalities, then an isomorphism between the two is impossible.

@Ivars: This would mean you have to make the distinction between the imaginary unit and an infinitesimal.

jaydfox Wrote:I never bought the distinction in density ... between rationals and realsIn my mind, there isn't any distinction in density, only in countability. Intuitively, it makes sense that the rationals are countable and the reals are not, but all other distinctions like power-sets and subsets and cardinalities and stuff, just confuses me.

Andrew Robbins