Question

I know that rational numbers are dense in real, but what is the purpose to say it, I mean what is the logic behind it, I know the proof but I don't understand that why do we need this statement/thm?

Answer 1

@KingGeorge @satellite73 any clue

Answer 2

I'm pretty sure it's used in the proof of the fact that for every \(x\in\mathbb{R}\), there is some sequence \((a_n)\in\mathbb{Q}\) that converges to \(x\). Beyond that, I'm not sure.