The Mathematical Experience |
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Page 250
... nonstandard universe containing pseu- doreals R * including a positive pseudoreal number c smaller than any number of the form 1 / n . That is , c is ... NONSTANDARD UNIVERSE STANDARD PORTION OF NONSTANDARD 250 Selected Topics in Mathematics.
... nonstandard universe containing pseu- doreals R * including a positive pseudoreal number c smaller than any number of the form 1 / n . That is , c is ... NONSTANDARD UNIVERSE STANDARD PORTION OF NONSTANDARD 250 Selected Topics in Mathematics.
Page 251
Philip J. Davis, Reuben Hersh. STANDARD UNIVERSE LANGUAGE L NONSTANDARD UNIVERSE STANDARD PORTION OF NONSTANDARD UNIVERSE Role of formal language in mediating between standard and nonstan- dard universes is por- trayed . Formal language ...
Philip J. Davis, Reuben Hersh. STANDARD UNIVERSE LANGUAGE L NONSTANDARD UNIVERSE STANDARD PORTION OF NONSTANDARD UNIVERSE Role of formal language in mediating between standard and nonstan- dard universes is por- trayed . Formal language ...
Page 253
... nonstandard ob- jects that correspond to standard objects have the feature that sentences about them are true ( in the nonstandard in- terpretation ) only if the same sentence is true with refer- ence to the standard object ( in the ...
... nonstandard ob- jects that correspond to standard objects have the feature that sentences about them are true ( in the nonstandard in- terpretation ) only if the same sentence is true with refer- ence to the standard object ( in the ...
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