The Mathematical Experience |
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Page 224
... natural numbers is not equivalent to the set of points on a line segment . ( See Appendix A. ) Thus there are at least two different kinds of infinity . The first , the infinity of the natural numbers ( and of any equivalent infinite ...
... natural numbers is not equivalent to the set of points on a line segment . ( See Appendix A. ) Thus there are at least two different kinds of infinity . The first , the infinity of the natural numbers ( and of any equivalent infinite ...
Page 225
... natural numbers , then it is easy to prove that 24 ( the set of all sets of natural numbers ) is equivalent to the continuum ( the set of all points on a line segment ) . In brief , 2N0 = C. At this point a question may occur to the ...
... natural numbers , then it is easy to prove that 24 ( the set of all sets of natural numbers ) is equivalent to the continuum ( the set of all points on a line segment ) . In brief , 2N0 = C. At this point a question may occur to the ...
Page 334
... natural numbers are given to us by a fundamental intui- tion , which is the starting point for all mathematics . He de- manded that all mathematics should be based constructively on the natural numbers . That is to say , mathematical ob ...
... natural numbers are given to us by a fundamental intui- tion , which is the starting point for all mathematics . He de- manded that all mathematics should be based constructively on the natural numbers . That is to say , mathematical ob ...
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