The Mathematical Experience |
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Page 191
... method is or whether we are confronted with an arithmetic rigamarole that is merely happenstance . He is encouraged , of course , by the word " Method " which promises more . The second part be- ginning " For each unity . " displays the ...
... method is or whether we are confronted with an arithmetic rigamarole that is merely happenstance . He is encouraged , of course , by the word " Method " which promises more . The second part be- ginning " For each unity . " displays the ...
Page 253
... method of infinitesimals , distin- guishing carefully between the nonstandard number ds / dt and its standard part v , avoids the contradiction ... method . Now the method of infinitesimals , or more generally the 253 Nonstandard Analysis.
... method of infinitesimals , distin- guishing carefully between the nonstandard number ds / dt and its standard part v , avoids the contradiction ... method . Now the method of infinitesimals , or more generally the 253 Nonstandard Analysis.
Page 362
... truths is attained by various methods , heuris- tic and " rigorous . " The heuristic method may be utterly convincing ; the rigorous method may leave us with nag- ging doubt . The Riemann Hypothesis W E TAKE AS OUR first example.
... truths is attained by various methods , heuris- tic and " rigorous . " The heuristic method may be utterly convincing ; the rigorous method may leave us with nag- ging doubt . The Riemann Hypothesis W E TAKE AS OUR first example.
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