No. For example, the field A of all algebraic numbers is algebraically closed, as is the field C of complex numbers, and both are extensions of the rationals Q. But A is countable and C is not: so they cannot be isomorphic.
No. For example, the field A of all algebraic numbers is algebraically closed, as is the field C of complex numbers, and both are extensions of the rationals Q. But A is countable and C is not: so they cannot be isomorphic.
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Originally Posted by rgep 