[steerablesafe]

You are of course right, reals are isomorphic to equivalence classes of Cauchy sequences on Q. But once you are dealing with equivalence classes of Cauchy sequences on Q you might as well give it a name. Maybe call it R.

[H8crilA]

His point is different. You cannot (by definition) ever write a "name", a formula, a rule, a lim expression, anything really, for a real that is not in the useful reals.