The Mathematical Experience |
From inside the book
Results 1-3 of 75
Page 231
... proved . That is to say , first , from any constructible collec- tion a of constructible sets ( A , B , . . . ) one can choose a constructible set Z consisting of at least one element each from A , B and so on . This is the axiom of ...
... proved . That is to say , first , from any constructible collec- tion a of constructible sets ( A , B , . . . ) one can choose a constructible set Z consisting of at least one element each from A , B and so on . This is the axiom of ...
Page 232
... proved from the other axioms but not whether they could be proved . Here the analogy with the parallel postulate in Euclidean geometry becomes particularly apt . That Euclid's axioms are consistent was taken for granted until quite ...
... proved from the other axioms but not whether they could be proved . Here the analogy with the parallel postulate in Euclidean geometry becomes particularly apt . That Euclid's axioms are consistent was taken for granted until quite ...
Page 364
... proved ) that all the zeros are somewhere between the imaginary axis and the line x = 1. To prove that they all lie exactly on x = would imply even more precise conclusions about the distribution of prime num- bers . It was a major ...
... proved ) that all the zeros are somewhere between the imaginary axis and the line x = 1. To prove that they all lie exactly on x = would imply even more precise conclusions about the distribution of prime num- bers . It was a major ...
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