The Mathematical Experience |
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Page 180
Philip J. Davis, Reuben Hersh. Algorithmic vs. Dialectic Mathematics = IN ORDER TO understand the difference in the point of view between algorithmic and dialectic mathematics we shall work with an example . Let us suppose that we have ...
Philip J. Davis, Reuben Hersh. Algorithmic vs. Dialectic Mathematics = IN ORDER TO understand the difference in the point of view between algorithmic and dialectic mathematics we shall work with an example . Let us suppose that we have ...
Page 181
... algorithmic mathematics . Solution II is the dialectic solution . In a certain sense , neither solution I nor solution II is a solution at all . Solution I gives us a better and better approximation , but whenever we stop we do not yet ...
... algorithmic mathematics . Solution II is the dialectic solution . In a certain sense , neither solution I nor solution II is a solution at all . Solution I gives us a better and better approximation , but whenever we stop we do not yet ...
Page 183
... Algorithmic mathematics is a tool for solving problems . Here we are con- cerned not only with the existence of a mathematical ob- ject , but also with the credentials of its existence . Dialectic mathematics is an intellectual game ...
... Algorithmic mathematics is a tool for solving problems . Here we are con- cerned not only with the existence of a mathematical ob- ject , but also with the credentials of its existence . Dialectic mathematics is an intellectual game ...
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