Remark 4

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

Algebra, V, p. 23, § 4. Algebraically closed extensions

Let K be a finite field and $\Omega$ an algebraic closure of $K$ . Then $\Omega$ is infinite ( $V,$ p. 20, Prop. 3); since every extension of finite degree of K is a finite field, $\Omega$ is an algebraic extension of infinite degree of $K$ .

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

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