The Mathematical Experience |
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Page 41
... mean anything , it's just a game , like chess , that we play with axioms and rules of inference . P.P .: Well , I didn't mean to be too hard on you . I'm sure it helps you in your research to imagine you're talking about something real ...
... mean anything , it's just a game , like chess , that we play with axioms and rules of inference . P.P .: Well , I didn't mean to be too hard on you . I'm sure it helps you in your research to imagine you're talking about something real ...
Page 80
... mean when it is said that a piece of mathe- matics is used or applied to mathematics itself ? For exam- ple , it may ... means that in order for you to understand the proof of this impossibility , you had better understand such and such ...
... mean when it is said that a piece of mathe- matics is used or applied to mathematics itself ? For exam- ple , it may ... means that in order for you to understand the proof of this impossibility , you had better understand such and such ...
Page 391
... means lacking in rigor , and yet the con- cept of rigor is itself defined intuitively rather than ri- gorously . ( 2 ) Intuitive means visual . Thus intuitive topology or ge- ometry differ from rigorous topology or geometry in two ...
... means lacking in rigor , and yet the con- cept of rigor is itself defined intuitively rather than ri- gorously . ( 2 ) Intuitive means visual . Thus intuitive topology or ge- ometry differ from rigorous topology or geometry in two ...
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