
Re: Double Induction  A brief note that may help
Posted:
Jul 16, 2013 7:55 PM


shouldn't (a.b), be in it
> Assume (a,b) not in S and let let c be the smallest c in N for which (c,b) not > > in S. Next let d be the smallest d in N for which (c,d) not in S. > > > > Case c = 1. Then (1,d) not in S and 1 < d. Thus (1,d1) in S and > > by hypthesis, (1,d) = (1, (d1)+1) in S, a contradiction. > > > > Case 1 < c. Then (c1,d) in S. Thus by hypothesis, (c,d) = ((c1)+1,d) in S > > a contradiction. > > > > Exercise. State and prove the base and induction steps > > of nfold induction. Can there be an aleph_0fold induction?

