This is a question relating to the notation. I think I have often seen the $a \in \mathbb R$ refer to that $a$ can be any element in $\mathbb R$. But of course, this is not necessary so, for example $a$ could be restricted to numbers 1 and 2, and still be in $\mathbb R$, in which case $a \in \mathbb R$ is also used and is more strictly correct.
So my question is, how can we specify that $a$ is restricted to some elements that belong in $\mathbb R$ and conversely that $a$ can be any element in $\mathbb R$? What notation should be used to differentiate the two cases?
In linear algebra there are some cases where it's desirable that $a$ can be any element in the real numbers, rather than just belonging into the set. That's the motivation for the question.