9. Recall from Section 2 that a field F is called an ordered field if there exists a subset P of F (called the set of positive elements) such that (a) sums and products of elements in P are in P, and (b) for each element a in F, one and only one of the following possibilities holds: a e P, a = 0, – a e P. Prove that the field of complex numbers is not an ordered field.

9. Recall from Section 2 that a field F is called an ordered field if there exists a subset P of F (called the set of positive elements) such that (a) sums and products of elements in P are in P, and (b) for each element a in F, one and only one of the following possibilities holds: a e P, a = 0, – a e P. Prove that the field of complex numbers is not an ordered field.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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