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.

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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 =
Prove that the field of complex numbers is not an ordered field.
0, - a e P.
Transcribed Image Text: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 = Prove that the field of complex numbers is not an ordered field. 0, - a e P.
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