[math-fun] induction from completeness?

I think I can derive the principle of induction for |N from the Dedekind-completeness of |R, via the supplementary assumption that 1 is the smallest positive integer, but I'm wondering if there's a subtle fallacy. Or maybe this is a standard derivation. Also, I'm wondering if one can derive induction from completeness without using the assumption that 1 is the smallest positive integer. My guess is "no", but I don't see off-hand a non-standard model that makes this clear. I can supply more details of my derivation tomorrow, if anyone likes. Jim