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.

15 pages; relaxed assumptions in Theorems A, C and Corollary B; new Corollaries 4.4, 5.4, 5.6 and Remark 5.5; numerous fixes and editorial improvements