Expert: Abe Mantell - 8/27/2010

Question
the rational numbers are countable many, and the real numbers are
uncountable many.  how many different types of infinity are there between these
two infinities?

Thanks for the assistance :)

Answer
The continuum hypothesis states that the cardinality of the rationals, denoted by aleph-null, is followed by the cardinality of the reals, denoted by C (for the continuum).  It has yet to be proven.  If true, then the answer to your question is "none."
For more, just search "continuum hypothesis."

Abe