The Mathematical Experience |
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Page 238
... infinitesimal calculus of Isaac Newton and Gottfried Wilhelm von Leibniz was reformu- lated by Karl Weierstrass without infinitesimals . Yet today it is mathematical logic , in its contemporary sophistication and power , that has ...
... infinitesimal calculus of Isaac Newton and Gottfried Wilhelm von Leibniz was reformu- lated by Karl Weierstrass without infinitesimals . Yet today it is mathematical logic , in its contemporary sophistication and power , that has ...
Page 242
... infinitesimal . In his Principia Mathematica , as in Archimedes ' On the Quadrature of the Parabola , results that were originally found by infini- tesimal methods are presented in a purely finite Euclidean fashion . Dynamics had become ...
... infinitesimal . In his Principia Mathematica , as in Archimedes ' On the Quadrature of the Parabola , results that were originally found by infini- tesimal methods are presented in a purely finite Euclidean fashion . Dynamics had become ...
Page 253
... infinitesimal and infinite num- bers are available ( in the nonstandard universe ) it can be proved that the area of the circle is the standard part of the sum ( in the nonstandard universe ) of infinitely many infin- itesimals . Here ...
... infinitesimal and infinite num- bers are available ( in the nonstandard universe ) it can be proved that the area of the circle is the standard part of the sum ( in the nonstandard universe ) of infinitely many infin- itesimals . Here ...
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