- continuum hypothesis
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The hypothesis which states that any infinite subset of must have the cardinality of either the set of natural numbers or of itself.
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continuum hypothesis
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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 — 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… … Philosophy dictionary
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
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
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 (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
