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 be the set of all Cauchy sequences where . Define the relation on as follows

Describe the equivalence classes. Show that the set of equivalence classes can be identified with the set of real numbers .

Thank you, thank you, thank you.