R as Q Vector space/Q to Q else zero/Exercise

Consider the function

$f\colon \mathbb {R} \longrightarrow \mathbb {R} ,$

which sends a rational number ${}q\in \mathbb {Q}$

to ${}q$, and all the irrational numbers to ${}0$. Is this a linear map? Is it compatible with multiplication by a scalar?

Create a solution