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- Well-Ordering and Mathematical Induction 3 answers
I want to prove that:
Well ordering principle ⟺ Complete Induction.
I am interested in both directions of the implication. That is, that if every non-empty set contains a least element then if a property P holds for all naturals less than n-1 it must hold for n. And viceversa.
I want the proof to be classical (I suspect this is quite difficult to prove constructively)