Quaternionic Versus Complex Probability Ampitude Distributions

From Science 2.0:

It is a mathematical fact that both the real numbers and the rational numbers contain an infinite amount of elements. It is possible to devise aprocedure that assigns a label containing a different natural number to every rational number. This is not possible for the real numbers. Technically this means that the set of real numbers has a higher cardinality than the set of rational numbers. In simple words it means that there are far more real numbers than there are rational numbers. Still both sets can densely cover a selected continuum, such as a line. However, the rational numbers leave open places,because infinite many real numbers fit between each pair of rational numbers.

Read the whole article