Monotonicity and a Taylor approximation theorem for transseries
Abstract
We show that the composition of omega-series by surreal numbers, or more generally by elements of any confluent field of transseries, is monotonic in its second argument. In particular, omega-series and LE-series interpreted as functions have the intermediate value property. We also deduce a Taylor approximation theorem for omega-series with maximal radius of validity.
Fields of Study & Subjects
Mathematical and Theoretical Analysis
Advanced Topology and Set Theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- White Rose Research Online (University of Leeds, The University of Sheffield, University of York)
- Publication date
- 12 January 2026
- Language
- EN