The Mathematical Experience |
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Page 140
... Mathematical Objects and Structures ; Existence I NFORMAL MATHEMATICAL discourse , as part of natural discourse , is composed of nouns , verbs , adjec- tives , etc. The nouns denote mathematical objects : for example , the number 3 ...
... Mathematical Objects and Structures ; Existence I NFORMAL MATHEMATICAL discourse , as part of natural discourse , is composed of nouns , verbs , adjec- tives , etc. The nouns denote mathematical objects : for example , the number 3 ...
Page 142
... object . Thus the real numbers R , a structure , may be thought of as an object when one takes the direct product R R to form pairs of real numbers . Standardized mathematical objects , structures , prob- lems , . . . are built into ...
... object . Thus the real numbers R , a structure , may be thought of as an object when one takes the direct product R R to form pairs of real numbers . Standardized mathematical objects , structures , prob- lems , . . . are built into ...
Page 408
... objects have definite properties . There are true facts about imaginary objects . From the Platonist point of view , Fact 1 is unacceptable . Since mathematical objects are what they are , in defiance of our ignorance or preferences ...
... objects have definite properties . There are true facts about imaginary objects . From the Platonist point of view , Fact 1 is unacceptable . Since mathematical objects are what they are , in defiance of our ignorance or preferences ...
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