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| '''Georg Cantor''' (born ] ] ], died ] ]) was a German ], best known for having created ] and the concept of transfinite numbers, including the ] and ] number classes. | '''Georg Cantor''' (born ] ] ] ], died ] ]) was a German ], best known for having created ] and the concept of transfinite numbers, including the ] and ] number classes. | ||
| He recognized that ] can have different sizes, distinguished between ] and ] sets and proved that the set of all ] is countable while the set of all ] is uncountable and hence strictly bigger. The proof uses his celebrated ]. In his later years, he tried in vain to prove the ]. By 1897, he had discovered several ] in elementary set theory. | He recognized that ] can have different sizes, distinguished between ] and ] sets and proved that the set of all ] is countable while the set of all ] is uncountable and hence strictly bigger. The proof uses his celebrated ]. In his later years, he tried in vain to prove the ]. By 1897, he had discovered several ] in elementary set theory. | ||
Revision as of 08:33, 20 April 2002
Georg Cantor (born St. Petersburg Russia March 3 1845, died January 6 1918) was a German mathematician, best known for having created set theory and the concept of transfinite numbers, including the cardinal and ordinal number classes.
He recognized that infinite sets can have different sizes, distinguished between countable and uncountable sets and proved that the set of all rational numbers is countable while the set of all real numbers is uncountable and hence strictly bigger. The proof uses his celebrated diagonal argument. In his later years, he tried in vain to prove the Continuum hypothesis. By 1897, he had discovered several paradoxes in elementary set theory.
Throughout the second half of his life he suffered from bouts of depression, which severely affected his ability to work and forced him to become hospitalized repeatedly. He started to publish about literature and religion, and developed his concept of the Absolute Infinite which he equated with God. He was impoverished during World War I and died in a sanatorium in 1918.
Cantor's innovative mathematics faced significant resistance during his lifetime. Modern mathematics completely accepts Cantor's work on transfinite sets and recognizes it as a paradigm shift of major importance.
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