Difference between revisions of "Georg Cantor"
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| − | '''Georg Cantor''' (1845-1918) was a [[German]] [[mathematician]] | + | '''Georg Cantor''' (1845-1918) was a [[German]] [[mathematician]] who created the field of [[Set_theory|Set Theory]]. His motivation was a religious one, as he sought to develop mathematical techniques for understanding the infinite. . |
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| + | Cantor's best known proof is his technique of [[Diagonalization|Cantorian Diagonalization]], a method useful to prove that the [[real numbers]] are larger in [[cardinality]] than the [[integers]]. He is also known for his [[Cantor_set|Cantor Set]]<ref>http://mathworld.wolfram.com/CantorSet.html</ref> and [[Cantor Intersection Theorem]]. | ||
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| + | The set of integers (or their equivalent) is the smallest infinite set. Cantor's "Continuum Hypothesis" is the conjecture that the set of all real numbers is the ''second'' smallest infinite set. | ||
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| + | Paul Cohen proved in the 1960s that the "Continuum Hypothesis" can neither be proved nor disproved within conventional (axiomatized) set theory. Stated another way, it is possible to develop a non-Cantorian set theory that negates the "Continuum Hypothesis." | ||
==References== | ==References== | ||
Revision as of 04:32, November 26, 2009
Georg Cantor (1845-1918) was a German mathematician who created the field of Set Theory. His motivation was a religious one, as he sought to develop mathematical techniques for understanding the infinite. .
Cantor's best known proof is his technique of Cantorian Diagonalization, a method useful to prove that the real numbers are larger in cardinality than the integers. He is also known for his Cantor Set[1] and Cantor Intersection Theorem.
The set of integers (or their equivalent) is the smallest infinite set. Cantor's "Continuum Hypothesis" is the conjecture that the set of all real numbers is the second smallest infinite set.
Paul Cohen proved in the 1960s that the "Continuum Hypothesis" can neither be proved nor disproved within conventional (axiomatized) set theory. Stated another way, it is possible to develop a non-Cantorian set theory that negates the "Continuum Hypothesis."