The Mathematical Experience |
From inside the book
Results 1-3 of 49
Page 141
... elements , 0 and 1. When a signa- ture has been subjected to a set of axioms that lay down re- quirements on its elements , then a mathematical structure emerges . Thus , a semigroup is < S , • > where • is a binary associative ...
... elements , 0 and 1. When a signa- ture has been subjected to a set of axioms that lay down re- quirements on its elements , then a mathematical structure emerges . Thus , a semigroup is < S , • > where • is a binary associative ...
Page 203
... elements which can be combined with one another to get other elements of G. The com- bination of two elements a and b in that order is indi- cated by a b . For every a and b in G , a · b is defined and is in G. · 2. For all elements a ...
... elements which can be combined with one another to get other elements of G. The com- bination of two elements a and b in that order is indi- cated by a b . For every a and b in G , a · b is defined and is in G. · 2. For all elements a ...
Page 204
... element a in G , there is an inverse element a - 1 in G such that a · a - 1 a - 1 · a = e . = Order : the number of elements in G is called the order of G. If the number of elements of G is finite then G is called a finite group ...
... element a in G , there is an inverse element a - 1 in G such that a · a - 1 a - 1 · a = e . = Order : the number of elements in G is called the order of G. If the number of elements of G is finite then G is called a finite group ...
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