Incredible Division prove different Infinities

Question:
http://uk.answers.yahoo.com/question/index?qid=20130217132342AAQdNDV

How does Incredible Division prove the existence of different Infinities?

Additional Details

(cardinality of Infinity in dimension-1) is compared to (cardinality of Infinity in dimension-2) at the dimension-3.
Can this be explained in different ways in detail?

'Baseless Riemann Hypothesis' math paper uses such infinity comparisons:
http://www.gsjournal.net/Science-Journal…

Answer: