$\mathbb Q(A) $ means the smallest subfield that contains $\mathbb Q\cup A$ where $A\subset\mathbb R.$ My question is: Let $I$ be an open interval subset of $\mathbb R.$ If $I\subset \mathbb Q(A)$ then $\mathbb R\subset\mathbb Q(A).$ Is it true ? I think yes, because since $\mathbb Q(A)$ is filed.
Any help will be appreciated greatly.