Question

Prove that for each a ∈ R and each n ∈ N, there exists a rational rn (subscript n) such that
|a − rn| <1/n.

Answer 1

I would solve the inequality for r_n

Answer 2

recall |f(x)|<a
where a is positive
implies
-a<f(x)<a

Answer 3

Thanks so much!!