Definition 1

Tag 06HP, permanent. Cite it as [Bourbaki, Tag 06HP].

Algebra, chapter V, § 3. Algebraic extensions

— An extension $E$ of a field $K$ is said to be algebraic (over $K$ ) if every element of $E$ is algebraic over $K$ . An extension $E$ of $K$ which is not algebraic is called transcendental (over $K$ ).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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