We know that the set of all limit points of $\Bbb Q$ is $\Bbb R$. This means that if $a \in \Bbb Q$, we can find a rational number as close to $a$ as we want. We also know that between every two rational numbers there exists an irrational number.
My question is:
Is $\Bbb R$ the set of all limit points of $\Bbb R \setminus \Bbb Q$ (of the irrational numbers)?
Can this be concluded only from the above?