The Mathematical Experience |
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Page 151
... proof . In college , a typical lecture in advanced mathe- matics , especially a lecture given by an instructor with “ pure ” interests , consists entirely of definition , theorem , proof , definition , theorem , proof , in solemn and ...
... proof . In college , a typical lecture in advanced mathe- matics , especially a lecture given by an instructor with “ pure ” interests , consists entirely of definition , theorem , proof , definition , theorem , proof , in solemn and ...
Page 299
... proofs of it . The theorem is the famous result of Pythag- oras that √2 is not a fraction . The first proof is the traditional proof . = Proof 1. One supposes that √2 = p / q where p and q are in- tegers . This equation is really an ...
... proofs of it . The theorem is the famous result of Pythag- oras that √2 is not a fraction . The first proof is the traditional proof . = Proof 1. One supposes that √2 = p / q where p and q are in- tegers . This equation is really an ...
Page 355
... proofs ( which is what Lakatos is talking about ) has been conclu- sively settled by the presence of a notion of infallible proof within metamathematics . ( This term of Hilbert's is now old - fashioned , if not obsolete , as a name for ...
... proofs ( which is what Lakatos is talking about ) has been conclu- sively settled by the presence of a notion of infallible proof within metamathematics . ( This term of Hilbert's is now old - fashioned , if not obsolete , as a name for ...
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