OOPS --- I misplaced a parenthesis. So sorry. Corrected version follows. I've growing fond of the following generalization of strong induction: ________________________________________________________________ Let universe U be a partially ordered set with the property that every subset of U has a MINIMAL element. If, forall n, (forall m<n, P(m)) => P(n) <=THIS LINE HAD MISPLACED PARENS then, forall n, P(n) ________________________________________________________________ (Proof requires axiom of choice. U generalizes the well-ordering principle where minimum is replaced by minimal.) I haven't seen this before, but I'm confident that's only because I'm ignorant. Could someone point me references to where induction is stated this way. Or can someone tell me if the property that every subset has a minimal element has a name? Thanks, David