On the intermediate value theorem over a non-Archimedean field

Abstract

The paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interval. The paper also investigates a few properties concerning the convergence of powerseries, Taylor's expansion around a point and the order of a zero.

Keywords

• Ordered fields
• Archimedean property
• Power series
• Intermediate value
• Extreme value