The Mathematical Experience |
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Page 204
... finite then G is called a finite group . Subgroup : A subset of G which is itself a group under the rule of combination in G is called a subgroup of G. Normal subgroup : If H is a subgroup of G , H is called nor- mal if for every g in G ...
... finite then G is called a finite group . Subgroup : A subset of G which is itself a group under the rule of combination in G is called a subgroup of G. Normal subgroup : If H is a subgroup of G , H is called nor- mal if for every g in G ...
Page 208
... finite groups is analogous to number the- ory in the following sense : just as every positive integer has a unique factorization into a product of primes , so every finite group can be “ factored ” in a certain sense ; it can be ...
... finite groups is analogous to number the- ory in the following sense : just as every positive integer has a unique factorization into a product of primes , so every finite group can be “ factored ” in a certain sense ; it can be ...
Page 249
... finite subset is logically consistent . So the entire collection of sentences is logically consistent ( since any deduction can make use of only a finite number of premises ) . By the com- pleteness theorem there is a ( nonstandard ) ...
... finite subset is logically consistent . So the entire collection of sentences is logically consistent ( since any deduction can make use of only a finite number of premises ) . By the com- pleteness theorem there is a ( nonstandard ) ...
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