The Mathematical Experience |
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Page 246
... real numbers . The momentum gathered by these foundational clarifica- tions led naturally to an assault on the logical foundations of the real - number system itself . This was a return after two and a half millenniums to the problem of ...
... real numbers . The momentum gathered by these foundational clarifica- tions led naturally to an assault on the logical foundations of the real - number system itself . This was a return after two and a half millenniums to the problem of ...
Page 250
... number c smaller than any number of the form 1 / n . That is , c is infin- itesimal . Moreover , c has all the properties of standard real numbers in a perfectly precise sense : any true statement about the standard reals that you can ...
... number c smaller than any number of the form 1 / n . That is , c is infin- itesimal . Moreover , c has all the properties of standard real numbers in a perfectly precise sense : any true statement about the standard reals that you can ...
Page 370
... real number system as understood by ordinary ( noncon- structivist ) mathematics . Since it would be hard to think of any branch of mathematics that does not depend crucially on the real numbers , this will show that Platonism is inti ...
... real number system as understood by ordinary ( noncon- structivist ) mathematics . Since it would be hard to think of any branch of mathematics that does not depend crucially on the real numbers , this will show that Platonism is inti ...
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 |
Common terms and phrases
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