Set-builder notation for a set that is either the complex or the real set

Question

If $F$ is either the set of real numbers $\mathbb{R}$ or the set of complex numbers $\mathbb{C}$, that is, if $F=\mathbb{R}$ or $F=\mathbb{C}$, is it correct to write $F=\{x:x\in\mathbb{R} \vee x\in\mathbb{C} \}$ ?

Answer 1

What you wrote down is $F = \mathbb{R} \cup \mathbb{C} = \mathbb{C}$.

But I think you meant to write $F \in \{\mathbb{R}, \mathbb{C}\}$.