The Mathematical Experience |
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Page 258
... function but by several , each valid in a dif- ferent region . The point is that for Euler and d'Alembert every function had a graph , but not every graph repre- sented a single function . Euler argued that any graph ( even if not given ...
... function but by several , each valid in a dif- ferent region . The point is that for Euler and d'Alembert every function had a graph , but not every graph repre- sented a single function . Euler argued that any graph ( even if not given ...
Page 264
... function . Dirichlet gave the defini- 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 ...
... function . Dirichlet gave the defini- 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 ...
Page 364
... function equals zero . Riemann conjectured that these roots all have real part = . Geometrically , they lie on the ... function on the line x . We still do not know if all of them are there . = 11 . It has been verified by calculations ...
... function equals zero . Riemann conjectured that these roots all have real part = . Geometrically , they lie on the ... function on the line x . We still do not know if all of them are there . = 11 . It has been verified by calculations ...
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