1. How is the Lemma 5.14 a restatement of Lemma 5.9? I don't see how the basis in Lemma 5.14 relates to Lemma 5.9
2. interesting to see that the complex number are two-dimensional over the real numbers.
It is obvious to see that the degree of real numbers over the rationals is infinite; what about the degree of the real numbers over the irrationals? would it be one?
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