Submission date: 23 October 2023

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.

Mathematics Subject Classification:

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Full text arXiv 2310.14873: pdf, ps.