Re: More complex numbers than reals?

FromTheRafters <FTR@nomail.afraid.org> wrote:

In a sense there are 'more' since the reals are all on the x axis line
whereas the 2D R x R space is filled with complex numbers. R is
contained in C. In another sense they are the same size set, C being
basically R by R in the same sense as Q being Z by Z).

Are there any other sizes of sets between countable Q and uncountable
R?

That is the Continuum Hypothesis, that asserts there are none.  It has
been shown that neither CH nor its negation can be proven in ZFC.  (But
don't ask me for the proof!)

How about between uncountable R and uncountable C?

These sets have the same cardinality, so no.

--
Alan Mackenzie (Nuremberg, Germany).