Basically I'm struggling to prove that if you take the indicator function $f$ on $\mathbb{Q}$ intersect $[0,1]$ and $\phi, \psi$ are step functions such that $\phi \leq f \leq \psi$ then $\phi \leq 0$ and $\psi \geq 0$ for all but finitely many $x$
As step functions can only be defined on intervals (by my definition I am working with) I'm trying to describe the places where the indicator function is 1
EDIT: so as $\mathbb{Q}$ is a set of discrete points, when we define a step function on $[0,1]$ can we can not find an interval such that the indicator function of $\mathbb{Q}$ intersect $[0,1]$ where it is 1, so can not find anywhere where $\phi > 0$? Unless we can define step functions pointwise?