The Mathematical Experience |
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Page 130
... tion from birds or oranges . " Arithmetic , " says Plato ( Republic VII.525 ) , “ has a very great and elevating effect , compelling the soul to reason about abstract number , and rebelling against the introduc- tion of visible or ...
... tion from birds or oranges . " Arithmetic , " says Plato ( Republic VII.525 ) , “ has a very great and elevating effect , compelling the soul to reason about abstract number , and rebelling against the introduc- tion of visible or ...
Page 248
... tion , between pseudostudents ( pictures of students ) . We could define the pseudorelation “ thinner than ” ( in quota- tion marks ) by saying that the two - inch square labeled " Harry Smith " is " thinner than " the two - inch square ...
... tion , between pseudostudents ( pictures of students ) . We could define the pseudorelation “ thinner than ” ( in quota- tion marks ) by saying that the two - inch square labeled " Harry Smith " is " thinner than " the two - inch square ...
Page 264
... tion which to this day is the most often used . A function y ( x ) is given if we have any rule which assigns a definite value y to every x in a certain set of points . " It is not neces- sary that y be subject to the same rule as ...
... tion which to this day is the most often used . A function y ( x ) is given if we have any rule which assigns a definite value y to every x in a certain set of points . " It is not neces- sary that y be subject to the same rule as ...
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