dorsal/arxiv
View SchemaMonotonicity and a Taylor approximation theorem for transseries
| Authors | Vincenzo Mantova |
|---|---|
| Categories | |
| ArXiv ID | 2601.07747vv1 |
| URL | https://arxiv.org/abs/2601.07747 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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 on positive infinite omega-series, or respectively LE-series, have the intermediate value property. We also deduce a Taylor approximation theorem for omega-series with maximal radius of validity.
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"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 on positive infinite omega-series, or respectively LE-series, have the intermediate value property. We also deduce a Taylor approximation theorem for omega-series with maximal radius of validity.",
"arxiv_id": "2601.07747",
"authors": [
"Vincenzo Mantova"
],
"categories": [
"math.LO",
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"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Monotonicity and a Taylor approximation theorem for transseries",
"url": "https://arxiv.org/abs/2601.07747",
"version": "v1"
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