The Mathematical Experience |
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Page 227
... given point there can be drawn precisely one line parallel to a given line . ( See the discussion of non - Eu- clidean geometry earlier in this chapter . ) The difficulty with this statement as an axiom is that it does not have the self ...
... given point there can be drawn precisely one line parallel to a given line . ( See the discussion of non - Eu- clidean geometry earlier in this chapter . ) The difficulty with this statement as an axiom is that it does not have the self ...
Page 258
... given the general solution of the problem . However , it is essential to understand that d'Alembert and his contemporaries meant by " function " what nowa- days would be called a " formula " or " analytic expression . " Euler pointed ...
... given the general solution of the problem . However , it is essential to understand that d'Alembert and his contemporaries meant by " function " what nowa- days would be called a " formula " or " analytic expression . " Euler pointed ...
Page 264
... 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 regards x throughout the interval , " wrote Dirichlet ; " indeed , one need ...
... 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 regards x throughout the interval , " wrote Dirichlet ; " indeed , one need ...
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