The Mathematical Experience |
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Page 362
... 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.
... 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.
Page 376
... rigorous logical proof that the numbers he gets from the machine are correct . First of all , the computing algorithm at the heart of the program cannot be guaranteed to work in all cases - only in all “ reasonable ” cases . That is to ...
... rigorous logical proof that the numbers he gets from the machine are correct . First of all , the computing algorithm at the heart of the program cannot be guaranteed to work in all cases - only in all “ reasonable ” cases . That is to ...
Page 391
... rigorous . This usage is itself not completely clear , for the meaning of " rigorous " it- self is never given precisely . We might say that in this usage intuitive means lacking in rigor , and yet the con- cept of rigor is itself ...
... rigorous . This usage is itself not completely clear , for the meaning of " rigorous " it- self is never given precisely . We might say that in this usage intuitive means lacking in rigor , and yet the con- cept of rigor is itself ...
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