I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

Cantor introduced fundamental constructions in set theory such as the power set of a set A which is the set of all possible subsets of A. Because the sets Sk were closed they contained their Limit points and the intersection of the infinite decreasing sequence of sets S S1 S2 S3.

Cantor establiGeorg Cantord the importance of one-to-one correspondence between the members of two sets defined infinite and well-ordered sets and proved that the real numbers are "more numerous" than the natural numbers. Cantor's recurring bouts of depression from 1884 to the end of his life have been blamed on the hostile attitude of many of his contemporaries though some have explained these episodes as probable manifestations of a bipolar disorder. David Hilbert defended it from its critics by famously declaring: "No one shall expel us from the Paradise that Cantor has created.