The cardinality of the reals has been known to be strictly greater than the cardinality of the naturals since Cantor. What the Continuum Hypothesis considers is the cardinality of the reals and the cardinality of the power set of the naturals. The power set of another set is the set of unique subsets of the first set. If the first set has cardinality of N, then the power set has cardinality 2^N. Thus, the reals can be considered to be exponentially more dense than the naturals.
Some intuition: while there may be N unique stocks on the NYSE, there could in theory be 2^N unique mutual funds that are based on the different combinations of stocks.
Some intuition: while there may be N unique stocks on the NYSE, there could in theory be 2^N unique mutual funds that are based on the different combinations of stocks.