- continuum hypothesis
- The hypothesis proposed by Cantor that there is no set with a cardinality greater than that of the natural numbers but less than the cardinality of the set of all subsets of the set of natural numbers (the power set of that set). The generalized continuum hypothesis is that the cardinality of any power set of an infinite set is the next highest cardinality after that of the set itself. Gödel proved in 1938 that the continuum hypothesis is consistent with classical set theory; the American mathematician Paul Cohen proved in 1963 that its negation is so too, i.e. the hypothesis is independent of the other axioms.

*Philosophy dictionary.
Academic.
2011.*

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**Continuum hypothesis**— This article is about the hypothesis in set theory. For the assumption in fluid mechanics, see Fluid mechanics. In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis, advanced by Georg Cantor in 1877[citation needed], about… … Wikipedia**continuum hypothesis**— Math. a conjecture of set theory that the first infinite cardinal number greater than the cardinal number of the set of all positive integers is the cardinal number of the set of all real numbers. [1935 40] * * * ▪ mathematics statement of… … Universalium**continuum hypothesis**— noun The hypothesis which states that any infinite subset of must have the cardinality of either the set of natural numbers or of itself … Wiktionary**continuum hypothesis**— Math. a conjecture of set theory that the first infinite cardinal number greater than the cardinal number of the set of all positive integers is the cardinal number of the set of all real numbers. [1935 40] … Useful english dictionary**The Continuum Hypothesis (album)**— Infobox Album Name = The Contimuum Hypothesis Type = studio Artist = Epoch of Unlight Released = Start date|2005 Recorded = October 27 November 4, 2004 Genre = Melodic death/Black metal Length = 53:11 Label = The End Records Producer = Reviews =… … Wikipedia**generalized continuum hypothesis**— noun The hypothesis that, for each ordinal <math> alpha</math>, there is no cardinal number strictly between <math> aleph alpha</math> and <math style= vertical align: 0%; >2^ aleph alpha</math>, i.e. <math… … Wiktionary**Continuum**— may refer to: Continuum (theory), anything that goes through a gradual transition from one condition, to a different condition, without any abrupt changes Contents 1 Linguistics 2 Mathematics … Wikipedia**Continuum mechanics**— Continuum mechanics … Wikipedia**Continuum (mathematics)**— In mathematics, the word continuum has at least two distinct meanings, outlined in the sections below. For other uses see Continuum.Ordered setThe term the continuum sometimes denotes the real line. Somewhat more generally a continuum is a… … Wikipedia**Continuum (set theory)**— In the mathematical field of set theory, the continuum means the real numbers, or the corresponding cardinal number, . The cardinality of the continuum is the size of the real numbers. The continuum hypothesis is sometimes stated by saying that… … Wikipedia