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). 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. | + | 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]] has since shown that the Continuum hypothesis is [[undecidable]] in [[Zermelo-Fraenkel]] Set Theory. |
[[category:set theory]] | [[category:set theory]] | ||
Revision as of 21:16, 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). 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 has since shown that the Continuum hypothesis is undecidable in Zermelo-Fraenkel Set Theory.
