# analysis – The Denseness of Q

Consider $$a, b ∈ R$$ where $$a < b$$. Use Denseness of $$mathbb Q$$ to show there are infinitely many rationals between $$a$$ and $$b$$.
I know $$P_1$$ is a true assertion since by the denseness of $$mathbb Q$$ there exists a rational, $$r_1$$ such that $$a. I can then assume $$P_n$$ is true and that there are $$n$$ distinct rationals between $$a$$ and $$b$$ of the form
$$a
This is where I’m stuck but I know I want to use the denseness of $$mathbb Q$$ again to say since $$a, I can find a rational $$r_{n+1}$$. At the same time, I don’t know what it is about $$mathbb Q$$ that allows me to say it.