At least a denumerable number of Infinities and rationals are dense but not complete

The work of Cantor http://www.math.vanderbilt.edu/~schectex/courses/infinity.pdf shows that there are at least aleph naught number of infinities.

The Power Set of a set cannot be put into one-to-one correspondence with the set and must be a larger infinity.

Between any two rational numbers another one can be found (dense).  The set of all rationals consists of a set of measure zero on the real line (not complete).