That would seem most familiar and comfortable to students. The only reason I didn't mention the decimal construction is that it favors base 10, and for mathematical aesthetics it's nice to have a "neutral" construction, like Cauchy sequences of rationals.

Of course, after constructing the reals as Cauchy sequences of rationals, one might want to show that Cauchy sequences of reals don't yield anything new (aka, the reals are complete). That leads students to feel with satisfaction that the reals is a natural object.

--Dan

Oh yeah? There are too damn many of them-- they're 1-1 with the continuous functions! --rwg UNREALISTIC UNCLARITIES

<< My favorite construction for the reals is to match the implicit "infin[i]te decimals" that we grew up with. It's the ground state, hence "intuitive". There's no harm in mentioning the alternatives, nor in emphasizing there are a bunch of equivalents.

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