Can someone help me with this problem? I wrote up a solution but the professor said that it was not what he wanted. He wants us to use the Cauchy sequence, or something like that. I don't remember exactly but I know he said Cauchy. (2 finals today, brain is fuzzy.)

The problem reads:

Let $\displaystyle \delta$ be the set of all Cauchy sequences $\displaystyle (r_i)$ where $\displaystyle r_i \epsilon \mathbb{Q}$. Define the relation on $\displaystyle \delta$ as follows

$\displaystyle (r_i)\sim(q_i)\ \Leftrightarrow \lim_{i \to \infty} (r_i-q_i)=0$

Describe the equivalence classes. Show that the set of equivalence classes can be identified with the set of real numbers $\displaystyle \mathbb{R}$.

Thank you, thank you, thank you.