My perspective differs. Dedekind cuts have a special case at all of the rationals. Which is weird. And the whole construct the completion using equivalence cl

My perspective differs. Dedekind cuts have a special case at all of the rationals. Which is weird. And the whole construct the completion using equivalence classes of sequences construction is one you'll encounter a bunch of times in topology. So it is worth learning it properly. Plus if you're into that kind of thing, you can also construct the p-adics this way. :-)