Problem

Prove that in any ordered field F, a2 + 1 > 0 for all a ∈ F. Conclude from this that if...

Prove that in any ordered field F, a2 + 1 > 0 for all aF. Conclude from this that if the equation x2 + 1 = 0 has a solution in a field, then that field cannot be ordered. (Thus it is not possible to define an order relation on the set of all complex numbers that will make it an ordered field.)

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Solutions For Problems in Chapter 3.11S