Continuum function

In mathematics, the continuum function is the function κ ↦ 2 κ {\displaystyle \kappa \mapsto 2^{\kappa }} on cardinals, i.e. raising 2 to the power of κ using cardinal exponentiation. Given a cardinal number, the cardinal function yields the cardinality of the power set of a set of the given cardinality.

In mathematics, the continuum function is the function κ ↦ 2 κ {\displaystyle \kappa \mapsto 2^{\kappa }} on cardinals, i.e. raising 2 to the power of κ using cardinal exponentiation.^[1] Given a cardinal number, the cardinal function yields the cardinality of the power set of a set of the given cardinality.

See also

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• Continuum hypothesis
• Cardinality of the continuum
• Beth number
• Easton's theorem
• Gimel function

References

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1. ^ Cody, Brent; Magidor, Menachem (February 2014). "On supercompactness and the continuum function". Annals of Pure and Applied Logic. 165 (2): 620–630. arXiv:1306.0449. doi:10.1016/j.apal.2013.09.001. ISSN 0168-0072.

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