MathDB

Suppose that

f,g:\mathbb{R}\to \mathbb{R}

satisfying f(r)\le g(r) \forall r\in \mathbb{Q} Does this imply f(x)\le g(x) \forall x\in \mathbb{R} if
(a)

f

and

g

are non-decreasing ? (b)

f

and

g

are continuous?

Problem Statement