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ISBN: 1139881701 1107366178 1107370906 1107361265 1107369800 1299403972 1107363713 0511892209 0511629141 9781107361263 9780511892202 0521312051 9780521312059 9780511629143 Year: 1986 Publisher: Cambridge Cambridge University Press
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The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the problems in the field. The topics covered include exponentiation and generalized e-numbers.
Surreal numbers. --- Number theory. --- Number study --- Numbers, Theory of --- Algebra --- Numbers, Surreal --- Number theory
ISBN: 1281798053 9786611798055 0080872522 0444702261 Year: 1987 Publisher: Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
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In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are d
Surreal numbers. --- Algebraic fields. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Numbers, Surreal --- Number theory --- Algebraic fields --- 517.1 --- Surreal numbers
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