
Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 20, 2012 7:20 AM


In article <513f89befeb44e3682108f2130314b70@x19g2000yqh.googlegroups.com>, Michael Ejercito <mejercit@hotmail.com> wrote:
>> Though this has the usual problem with multiple representations. For >> example, both 0.1 and 0.00909090... map to (0.1, 0).
> That is correct. This would imply that each complex number maps >onto MULTIPLE real numbers, and certainly the reals can not have a >GREATER cardinality than the complexes.
Given a surjection both ways, the dual Schroder Bernstein theorem shows that there is a bijection. This however relies on the axiom of choice.
If we take the interleaved digits as a base11 number we have an injection both ways, and standard Schroder Bernstein gives us a bijection.
 Richard

