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Meaning of "continuum hypothesis" in the English dictionary

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DICTIONARY
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PRONUNCIATION OF CONTINUUM HYPOTHESIS

continuum hypothesis play
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GRAMMATICAL CATEGORY OF CONTINUUM HYPOTHESIS

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Continuum hypothesis is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES CONTINUUM HYPOTHESIS MEAN IN ENGLISH?

Continuum hypothesis

In mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1878, about the possible sizes of infinite sets. It states: There is no set whose cardinality is strictly between that of the integers and the real numbers. Establishing the truth or falsehood of this hypothesis is the first of Hilbert's 23 problems presented in the year 1900. Τhe answer to this problem is independent of ZFC set theory, so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940. The name of the hypothesis comes from the term the continuum for the real numbers.

Definition of continuum hypothesis in the English dictionary

The definition of continuum hypothesis in the dictionary is the assertion that there is no set whose cardinality is greater than that of the integers and smaller than that of the reals.

WORDS THAT BEGIN LIKE CONTINUUM HYPOTHESIS

continuingly
continuities
continuity
continuity announcer
continuity girl
continuity man
continuo
continuous
continuous assessment
continuous creation
continuous miner
continuous processing
continuous spectrum
continuous stationery
continuous waves
continuous-release
continuously
continuousness
continuum
contline

WORDS THAT END LIKE CONTINUUM HYPOTHESIS

alternative hypothesis
anthesis
antithesis
biosynthesis
diathesis
doctoral thesis
genesis
hypothesis
in parenthesis
Lachesis
metathesis
nucleosynthesis
null hypothesis
parenthesis
PhD thesis
photosynthesis
prosthesis
prothesis
synthesis
thesis
working hypothesis

Synonyms and antonyms of continuum hypothesis in the English dictionary of synonyms

SYNONYMS

Translation of «continuum hypothesis» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF CONTINUUM HYPOTHESIS

Find out the translation of continuum hypothesis to 25 languages with our English multilingual translator.
The translations of continuum hypothesis from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «continuum hypothesis» in English.

Translator English - Chinese

连续统假设
1,325 millions of speakers

Translator English - Spanish

hipótesis del continuo
570 millions of speakers

English

continuum hypothesis
510 millions of speakers

Translator English - Hindi

सातत्य परिकल्पना
380 millions of speakers
ar

Translator English - Arabic

فرضية متصلة
280 millions of speakers

Translator English - Russian

континуум-гипотеза
278 millions of speakers

Translator English - Portuguese

hipótese do contínuo
270 millions of speakers

Translator English - Bengali

ধারাবাহিক অনুমান
260 millions of speakers

Translator English - French

hypothèse du continu
220 millions of speakers

Translator English - Malay

Hipotesis kontinum
190 millions of speakers

Translator English - German

Kontinuumshypothese
180 millions of speakers

Translator English - Japanese

連続体仮説
130 millions of speakers

Translator English - Korean

연속체 가설
85 millions of speakers

Translator English - Javanese

Hipotesis terus-terusan
85 millions of speakers
vi

Translator English - Vietnamese

giả thuyết liên tục
80 millions of speakers

Translator English - Tamil

தொடர்ச்சியான கருதுகோள்
75 millions of speakers

Translator English - Marathi

सातत्य संकल्पना
75 millions of speakers

Translator English - Turkish

Sürekli hipotez
70 millions of speakers

Translator English - Italian

ipotesi del continuo
65 millions of speakers

Translator English - Polish

hipoteza continuum
50 millions of speakers

Translator English - Ukrainian

континуум - гіпотеза
40 millions of speakers

Translator English - Romanian

ipoteza continuum
30 millions of speakers
el

Translator English - Greek

υπόθεση του Συνεχούς
15 millions of speakers
af

Translator English - Afrikaans

kontinuum hipotese
14 millions of speakers
sv

Translator English - Swedish

kontinuum hypotes
10 millions of speakers
no

Translator English - Norwegian

kontinuum hypotesen
5 millions of speakers

Trends of use of continuum hypothesis

TRENDS

TENDENCIES OF USE OF THE TERM «CONTINUUM HYPOTHESIS»

The term «continuum hypothesis» is normally little used and occupies the 134.629 position in our list of most widely used terms in the English dictionary.
0
100%
FREQUENCY
Little used
37
/100
The map shown above gives the frequency of use of the term «continuum hypothesis» in the different countries.
Principal search tendencies and common uses of continuum hypothesis
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «continuum hypothesis».

FREQUENCY OF USE OF THE TERM «CONTINUUM HYPOTHESIS» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «continuum hypothesis» during the past 500 years. Its implementation is based on analysing how often the term «continuum hypothesis» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about continuum hypothesis

EXAMPLES

10 ENGLISH BOOKS RELATING TO «CONTINUUM HYPOTHESIS»

Discover the use of continuum hypothesis in the following bibliographical selection. Books relating to continuum hypothesis and brief extracts from same to provide context of its use in English literature.
1
The Consistency of the Axiom of Choice and of the ...
Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century.
Kurt Gödel, George William Brown, 1940
2
Set Theory and the Continuum Hypothesis
In this volume, the distinguished mathematician offers an exposition of set theory and the continuum hypothesis that employs intuitive explanations as well as detailed proofs.
Paul J. Cohen, 2012
3
The Consistency of the Continuum Hypothesis by Kurt Gödel
Previously published: Princeton University Press, 1940.
Kurt Gödel, 2008
4
Set Theory and the Continuum Problem
A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
Raymond Merrill Smullyan, Melvin Chris Fitting, 2010
5
CRC Concise Encyclopedia of Mathematics, Second Edition
Continuum Hypothesis MANIFOLD. The map n is CONTINUOUS. It has no SMOOTH STRUCTURE Or METRIC. See also BUNDLE, MANIFOLD, METRIC ( BUNDLE), VECTOR BUNDLE Continuously Differentiable Function The space of  ...
Eric W. Weisstein, 2002
6
The Axiom of Determinacy, Forcing Axioms, and the ...
This is the revised and updated second edition of a well-established research monograph on the axiom of determinacy, written by an expert in the field.
W. Hugh Woodin, 2010
7
Handbook of Logic and Proof Techniques for Computer Science
In other words, it is consistent with the axioms to suppose that the continuum hypothesis is false. (It had been known for some time — see below — that it is consistent with the axioms of set theory to suppose that CHis true.) The generalized ...
Steven G. Krantz, 2002
8
How Mathematicians Think: Using Ambiguity, Contradiction, ...
Kurt Go ̈del14 proved that the continuum hypothesis cannot be disproved using the standard Zermelo-Fraenkel axioms for set theory (including the axiom of choice). Twenty-three years later Paul Cohen15 showed that the continuum ...
William Byers, 2010
9
Encyclopaedia of Mathematics, Supplement III
The first substantial result was Godel 's relative consistency result [7], [8], that if ZF is consistent, then so also is ZFC (and this together with Cantor's continuum hypothesis; cf. also Consistency). P. Cohen [1], [2], in famous work leading to the  ...
Michiel Hazewinkel, 2001
10
Truth and Other Enigmas
One who holds that, despite these results, the continuum hypothesis must be determinately either true or false is in effect taking the view that, when we do set theory, we have in mind some completely determinate mathematical structure : in  ...
Michael Dummett, 1978

10 NEWS ITEMS WHICH INCLUDE THE TERM «CONTINUUM HYPOTHESIS»

Find out what the national and international press are talking about and how the term continuum hypothesis is used in the context of the following news items.
1
Continuum Streaming New Track "A Surreal Descent"
... surgically precise compositions based conceptually on the mysteries of the infinite and the unsolved theories of the "continuum hypothesis.". «Metal Underground, Mar 15»
2
Continuum Reveals New Album
... steeped conceptually in the mysteries of the infinite and the early but no-less-relevant and unsolved theories of the "continuum hypothesis.". «Metal Underground, Feb 15»
3
CSUN Prof. Luciana Lagana Will Receive Best Trailer Award for Her …
Community-dwelling adults versus older adults: Psychopathology and the continuum hypothesis. Educational Gerontology, 38(6), 412-428, doi: ... «PR Web, Feb 15»
4
Dr. Luciana Lagana and Producer Del Weston Tackle Aging and …
Community-dwelling adults versus older adults: Psychopathology and the continuum hypothesis. Educational Gerontology, 38(6), 412-428, doi: ... «PR Web, Jan 15»
5
The Continuum Hypothesis and the search for Mathematical Infinity …
Does the Continuum Hypothesis have an answer? This question is pointed out by professor W. Hugh Woodin. He admits that 15 years ago he ... «Institute for Ethics and Emerging Technologies, Jan 15»
6
Taking Infestation with a Grain of Salt
“There's an idea in plant biology called the 'compensatory continuum hypothesis' whereby plants can compensate for grazing by growing more, ... «SDSU Newscenter, Oct 14»
7
Maths From An Extra Terrestrial Civilization - What Could It Be Like …
Continuum hypothesis - why does our maths say that we can never know whether or not there are other orders of infinity between the number of ... «Science 2.0, Jun 14»
8
A Century On, This Math Prodigy's Formulas Are Finally Unravelled
... about it is called the continuum hypothesis). The “enlarged infinity” is because of all the irrational numbers – there are just too many of them! «Discover Magazine, Jun 14»
9
Dispute over Infinity Divides Mathematicians
Chief among the holes is the continuum hypothesis, a 140-year-old statement about the possible sizes of infinity. As incomprehensible as it ... «Scientific American, Dec 13»
10
When a hypothesis is neither true nor false
Cantor's Continuum Hypothesis is a statement regarding sizes of infinity. To see how infinity can have more than one size, let's first ask ... «Salon, Jul 13»

REFERENCE
« EDUCALINGO. Continuum hypothesis [online]. Available <https://educalingo.com/en/dic-en/continuum-hypothesis>. May 2024 ».
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