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 '''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). Cantor died without knowing the answer to his conjecture. [[Kurt Godel]] and [[Paul Cohen]] has since shown that the Continuum hypothesis is [[undecidable]] in [[Zermelo-Fraenkel]] Set Theory. |
[[category:set theory]] | [[category:set theory]] | ||
Revision as of 19:56, November 27, 2008
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). Cantor died without knowing the answer to his conjecture. Kurt Godel and Paul Cohen has since shown that the Continuum hypothesis is undecidable in Zermelo-Fraenkel Set Theory.