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Preprints, Working Papers, ... Year : 2021

The hyperserial field of surreal numbers

Abstract

For any ordinal α>0, we show how to define a hyperexponential E_(ω^α) and a hyperlogarithm L_(ω^α) on the class No^(>,≻) 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.
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Dates and versions

hal-03232836 , version 1 (22-05-2021)

Identifiers

  • HAL Id : hal-03232836 , version 1

Cite

Vincent Bagayoko, Joris van der Hoeven. The hyperserial field of surreal numbers. 2021. ⟨hal-03232836⟩
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