Algebraic Closure of Rational Number Field is Algebraic Number Field

Theorem

Let $\Q$ denote the field of rational numbers.

Let $\Bbb A$ denote the field of algebraic numbers.

The algebraic closure of $\Q$ is $\Bbb A$.

Proof

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Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): algebraically closed (algebraic closure)