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Transfinite Function Iteration and Surreal Numbers
Advances in Applied Mathematics, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Beyer, W.A., Louck, J.D.
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Duality, Matroids, Qubits, Twistors, and Surreal Numbers [PDF]
Frontiers in Physics, 2018 We show that via the Grassmann-Plücker relations, the various apparent unrelated concepts, such as duality, matroids, qubits, twistors and surreal numbers are, in fact, deeply connected. Moreover, we conjecture the possibility that these concepts may be considered as underlying mathematical structures in quantum gravity.
J A Nieto
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The Exponential-Logarithmic Equivalence Classes of Surreal Numbers [PDF]
Order, 2014 In his monograph, H. Gonshor showed that Conway's real closed field of surreal numbers carries an exponential and logarithmic map. Subsequently, L. van den Dries and P. Ehrlich showed that it is a model of the elementary theory of the field of real numbers with the exponential function.
Salma Kuhlmann +2 more
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Surreal numbers, derivations and transseries [PDF]
Journal of the European Mathematical Society, 2018 Several authors have conjectured that Conway’s field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy type. In this paper we give a complete positive solution to both problems. We also show that with this new differential
Berarducci, A, Mantova, V
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Surreal numbers as hyperseries
, 2023 Surreal numbers form the ultimate extension of the field of real numbers with infinitely large and small quantities and in particular with all ordinal numbers. Hyperseries can be regarded as the ultimate formal device for representing regular growth rates at infinity. In this paper, we show that any surreal number can naturally be regarded as the value
Bagayoko, Vincent, van der Hoeven, Joris
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Conway’s field of surreal numbers [PDF]
Transactions of the American Mathematical Society, 1985 Conway introduced the Field N o {\mathbf {No}}
Norman L. Alling
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Some Mathematical and Physical Remarks on Surreal Numbers
Journal of Modern Physics, 2016 19 pages, Latex, to be published in Journal of Modern ...
Juan Antonio Nieto
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The surreal numbers as a universal $H$-field [PDF]
Journal of the European Mathematical Society, 2019 We show that the natural embedding of the differential field of transseries into Conway’s field of surreal numbers with the Berarducci–Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci–Mantova derivation.
Aschenbrenner, Matthias +2 more
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Surreal Analysis: An Analogue of Real Analysis for Surreal Numbers
Journal of Logic and Analysis, 2014 Summary: The class \textbf{No} of surreal numbers, which John Conway discovered while studying combinatorial games, possesses a rich numerical structure and shares many arithmetic and algebraic properties with the real numbers. Some work has also been done to develop analysis on \textbf{No}.
Simon Rubinstein-Salzedo +1 more
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Fields of surreal numbers and exponentiation [PDF]
Fundamenta Mathematicae, 2001 The authors consider sets of the form: all surreal numbers whose length is less than a given ordinal. They show that the ordinal determines certain algebraic properties of the corresponding set. In particular, the set is a field iff the ordinal is an epsilon-number. Furthermore, such a field will be closed under exponentiation. The key lemmas establish
van den Dries, Lou, Ehrlich, Philip
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