Analysis involving closed intervals and rationality

Question

Can someone help me prove this problem? Prove that every closed interval $[a,b]$ is a subset of $\mathbb{R}$ contains at least one rational number.

"dual of" Analysis proof about irrational numbers – amWhy Apr 26 '13 at 17:43 — amWhy, Apr 26 '13 at 17:43

score 0 · Answer 1 · answered Apr 26 '13 at 17:51

0

Let $\frac1{n}<b-a$ then for some $ m \in \mathbb{Z}$ , we have $\frac m{n}\in [a,b]$ ..

answered Apr 26 '13 at 17:51

Halil Duru

1 Answers1