Definition:Smallest Field containing Subfield and Complex Number

Definition
Let $F$ be a field.

Let $\theta \in \C$ be a complex number.

Let $S$ be the intersection of all fields such that:
 * $S \subseteq F$
 * $\theta \in F$

Then $S$ is denoted $\map F \theta$ and referred to as the smallest field containing $F$ and $\theta$.