# Continuum function

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In mathematics, the '''continuum function''' is the function <math>\kappa\mapsto 2^\kappa</math> on [cardinal](/source/Cardinal_number)s, i.e. raising 2 to the power of ''&kappa;'' using [cardinal exponentiation](/source/cardinal_exponentiation).<ref>{{Cite journal |last=Cody |first=Brent |last2=Magidor |first2=Menachem |author2link = Menachem Magidor|date=February 2014 |title=On supercompactness and the continuum function |url=https://doi.org/10.1016/j.apal.2013.09.001 |journal=[Annals of Pure and Applied Logic](/source/Annals_of_Pure_and_Applied_Logic) |volume=165 |issue=2 |pages=620–630 |doi=10.1016/j.apal.2013.09.001 |issn=0168-0072|arxiv=1306.0449 }}</ref> Given a cardinal number, the cardinal function yields the cardinality of the [power set](/source/power_set) of a set of the given cardinality.

==See also==
*[Continuum hypothesis](/source/Continuum_hypothesis)
*[Cardinality of the continuum](/source/Cardinality_of_the_continuum)
*[Beth number](/source/Beth_number)
*[Easton's theorem](/source/Easton's_theorem)
*[Gimel function](/source/Gimel_function)

Category:Cardinal numbers

== References ==
{{Reflist}}{{settheory-stub}}

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Adapted from the Wikipedia article [Continuum function](https://en.wikipedia.org/wiki/Continuum_function) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Continuum_function?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.