The Mathematical Experience |
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Page 231
Philip J. Davis, Reuben Hersh. tinuum hypothesis . Thus , as we shall explain , there now exists a complete solution of the continuum problem . To Gödel's discovery that the continuum hypothesis is not dis- provable is added the fact ...
Philip J. Davis, Reuben Hersh. tinuum hypothesis . Thus , as we shall explain , there now exists a complete solution of the continuum problem . To Gödel's discovery that the continuum hypothesis is not dis- provable is added the fact ...
Page 235
... continuum hypoth- esis is false we must add to M not just one new element a ... hypothesis is false . The new ele- ments , which in N ' play the role of ... continuum hypothesis is false , it follows that we can add to our ordinary ...
... continuum hypoth- esis is false we must add to M not just one new element a ... hypothesis is false . The new ele- ments , which in N ' play the role of ... continuum hypothesis is false , it follows that we can add to our ordinary ...
Page 236
... continuum hypothesis remains unde- cided . Cohen and Gödel proved that the axioms of Zer- melo - Frankel set theory are not sufficient to decide it . If we believe sets are real , then we may be convinced that the continuum hypothesis ...
... continuum hypothesis remains unde- cided . Cohen and Gödel proved that the axioms of Zer- melo - Frankel set theory are not sufficient to decide it . If we believe sets are real , then we may be convinced that the continuum hypothesis ...
Other editions - View all
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |
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abstract aesthetic algebra algorithmic analysis analytic answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex conjecture construct continuum hypothesis course definition differential equations elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hilbert human hypercube hypersquares idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry non-Riemannian nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line symbols theorem thing tion triangle true truth universe words zero