continuum hypothesis

collocation in English

meaningsofcontinuumandhypothesis

These words are often used together. Click on the links below to explore the meanings. Or,see other collocations withcontinuum.
continuum
noun[C]
uk
/kənˈtɪn.ju.əm/us
/kənˈtɪn.ju.əm/
something that changes in character gradually or in very slight stages without any clear ...
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hypothesis
noun[C]
uk
/haɪˈpɒθ.ə.sɪs/us
/haɪˈpɑː.θə.sɪs/
an idea or explanation for something that is based on known facts but has not yet ...
See more athypothesis

(Definition ofcontinuumandhypothesisfrom theCambridge English Dictionary© Cambridge University Press)

Examplesofcontinuum hypothesis

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The 148 linguistic and cultural maps permit the exploration of many questions - including thecontinuumhypothesisitself; paradoxically, considerable data here seem to disconfirm the hypothesis.
From theCambridge English Corpus
Assume the generalisedcontinuumhypothesis.
From theCambridge English Corpus
Thecontinuumhypothesisis closely related to many statements in analysis, point set topology and measure theory.
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This is a generalization of thecontinuumhypothesissince the continuum has the same cardinality as the power set of the integers.
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This question leads to the famouscontinuumhypothesis.
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Many large cardinal axioms were studied but thecontinuumhypothesisremained independent from them.
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This dispute may be better understood when considering specific examples, such as thecontinuumhypothesis.
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There was only one paper, on thecontinuumhypothesis, that she was unable to repair.
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The theory he developed involves a controversial argument that thecontinuumhypothesisis false.
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If the generalizedcontinuumhypothesisholds, then a cardinal is strongly inaccessible if and only if it is weakly inaccessible.
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The conjecture is a trivial consequence of thecontinuumhypothesis; so this axiom is often excluded in work on the conjecture.
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Consequently, assumption of thecontinuumhypothesiscan lead to results which are not of desired accuracy.
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Two famous statements in set theory are the axiom of choice and thecontinuumhypothesis.
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He used his axioms in his 1940 monograph on the relative consistency of global choice and the generalizedcontinuumhypothesis.
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This is not yet the falsification of thecontinuumhypothesis.
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One idea is that the set universe ought to be rich, with many sets, which leads to thecontinuumhypothesisbeing false.
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It is then wrong to stipulate, a priori and for philosophical reasons, that thecontinuumhypothesisis true or false.
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That said, under the right circumstances, thecontinuumhypothesisproduces extremely accurate results.
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Those problems for which thecontinuumhypothesisdoes not allow solutions of desired accuracy are solved using statistical mechanics.
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A trivial consequence of thecontinuumhypothesisis that a complete theory with less than continuum many nonisomorphic countable models can have only countably many.
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These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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