Difference between revisions of "Continuum hypothesis"
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| − | The '''Continuum hypothesis''' is a conjecture by [[Georg Cantor]] which states that the cardinality of the real numbers equals that of <math>\mathcal{P}(\mathbb{N})</math>, the power set of the [[natural numbers]]. The cardinality of this set is denoted with the Hebrew letter <math>\aleph</math>. [[Kurt Godel]] and [[ | + | The '''Continuum hypothesis''' is a conjecture by [[Georg Cantor]] which states that the cardinality of the real numbers equals that of <math>\mathcal{P}(\mathbb{N})</math>, the power set of the [[natural numbers]]. The cardinality of this set is denoted with the Hebrew letter <math>\aleph</math>. [[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 18:47, April 13, 2007
The Continuum hypothesis is a conjecture by Georg Cantor which states that the cardinality of the real numbers equals that of , the power set of the natural numbers. The cardinality of this set is denoted with the Hebrew letter . Kurt Godel and Paul Cohen has since shown that the Continuum hypothesis is undecidable in Zermelo-Fraenkel Set Theory.
