The hyperserial field of surreal numbers


For any ordinal , we show how to define a hyperexponential and a hyperlogarithm on the class of positive infinitely large surreal numbers. Such functions are archetypes of extremely fast and slowly growing functions at infinity. We also show that the surreal numbers form a so-called hyperserial field for our definition.

Authors: Vincent Bagayoko, Joris van der Hoeven

Keywords: hyperserial field, surreal numbers, surreal substructures

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