[Classical Geometries] How do you solve this question? Thank you DefinitionAn ordered field is a field F, together with a subset P, whose elements are calledpositive, satisfying:(i) If a, b e P, then a + b e P and ab € P.(ii) For any a € F, one and only one of the following holds: a e P; a = 0; −a = P.Here are a few elementary properties of an ordered field.Proposition 15.1Let F, P be an ordered field. Then:(a) 1 € P, i.e., 1 is a positive element.(b) F has characteristic 0.(c) The smallest subfield of F containing 1 is isomorphic to the rational numbers Q.(d) For any a #0 € F, a² € P. 15.1 If a > 0 in an ordered field F, show that a-¹ > 0 also.

Introduction: An ordered field is a field (a set of numbers with two operations, addition and…

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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