# Are these two definitions of separable extension equivalent?

Definition1 - wikipedia

Let $E/F$ be an algebraic extension. Then $E/F$ is separable iff for each $\alpha\in E$, the minimal polynomial of $\alpha$ over $F$ is separable.

Definition 2 - Lang

Let $E/F$ be an algebraic extension. Then $E/F$ is separable iff $[E:F]=[E:F]_{sep}$.

I know if the extension is finite, then these two definitions are equivalent. However, if the extension is not finite, are these definitions still equivalent? And which is the standard one?