| 31. | In the 1960s, Cohen proved that neither is provable from ZF, and the continuum hypothesis cannot be proved from ZFC.
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| 32. | He used his axioms in his 1940 monograph on the relative consistency of global choice and the generalized continuum hypothesis.
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| 33. | His continuum hypothesis is the proposition that \ mathfrak { c } is the same as \ aleph _ 1.
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| 34. | Using a Eulerian model ( the continuum hypothesis ), fluid motion can be described in terms of acceleration or velocity.
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| 35. | If the generalized continuum hypothesis holds, then a cardinal is strongly inaccessible if and only if it is weakly inaccessible.
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| 36. | The continuum hypothesis postulates that the cardinality of the continuum is equal to \ aleph _ 1 which is regular.
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| 37. | In 1904, at the third International Congress of Mathematicians at Heidelberg, KQnig gave a talk to disprove Cantor's continuum hypothesis.
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| 38. | However, the truth of the continuum hypothesis depends on the version of set theory you are using and so is undecidable.
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| 39. | The Platonist claim that every intelligence must produce prime numbers, pi and the continuum hypothesis is an example of simple anthropomorphism,
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| 40. | The continuum hypothesis is a statement in the language of ZFC that is not provable within ZFC, so ZFC is not complete.
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