I know we have accepted Cantor's ideas a long time ago and many mathematicians use sets and infinities without ever realizing that thinking about sets and infinities intuitively fails, because there are many paradoxes associated with naive set theory. However, why did mathematicians such as Kronecker regarded Cantor's ideas as absurdities, and as I remember accused Cantor of impiety and the corruption of youth. Also, I believe Poincare did not like Cantor's ideas, yet he did a lot of research in topology, which is based on the notion of an open set. Can any one explain why so many people apposed Cantor's ideas? Why is the traditional view of infinite so appealing although Cantor's proofs are valid.
closed as not constructive by Thomas, hardmath, rschwieb, Norbert, Pedro Tamaroff Nov 14 '12 at 1:41
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