Difference between revisions of "Continuum hypothesis"
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| − | The '''Continuum hypothesis''' is a conjecture by [[Georg Cantor]] which states that there is no set with [[cardinality]] greater than all the [[natural number]]s but less than the cardinality of the [[real number]]s (Continuum). The cardinality of such a set would be denoted by the Hebrew letter <math>\aleph</math>. Cantor died without knowing the answer to his conjecture. [[Kurt Godel]] and [[Paul Cohen]] | + | The '''Continuum hypothesis''' is a conjecture by [[Georg Cantor]] which states that there is no set with [[cardinality]] greater than all the [[natural number]]s but less than the cardinality of the [[real number]]s (Continuum). The cardinality of such a set would be denoted by the Hebrew letter <math>\aleph</math>. Cantor died without knowing the answer to his conjecture. [[Kurt Godel]] and [[Paul Cohen]] have since shown that the Continuum hypothesis is [[undecidable]] in [[Zermelo-Fraenkel]] Set Theory. |
[[category:set theory]] | [[category:set theory]] | ||
Revision as of 02:01, February 9, 2009
The Continuum hypothesis is a conjecture by Georg Cantor which states that there is no set with cardinality greater than all the natural numbers but less than the cardinality of the real numbers (Continuum). The cardinality of such a set would be denoted by the Hebrew letter 
. Cantor died without knowing the answer to his conjecture. Kurt Godel and Paul Cohen have since shown that the Continuum hypothesis is undecidable in Zermelo-Fraenkel Set Theory.
