Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/5/84; site ittvax.UUCP Path: utzoo!linus!decvax!ittvax!allenm From: allenm@ittvax.UUCP (Allen Matsumoto) Newsgroups: net.math Subject: Re: Re: Induction help, please? Message-ID: <1514@ittvax.UUCP> Date: Mon, 8-Oct-84 11:31:49 EDT Article-I.D.: ittvax.1514 Posted: Mon Oct 8 11:31:49 1984 Date-Received: Tue, 9-Oct-84 20:24:48 EDT References: <5264@yale.ARPA> <470@foxvax1.UUCP> Organization: ITT-ATC, Stratford Ct. Lines: 50 I can't decide if this is a simple reply or a parody of meta-induction. > > > When I was a kid, I also had problems with induction. I just > couldn't understand where to start or even why the thing > worked. I eventually became proficient in induction in the > following manner: I found a book that contained one induction > problem that I could solve. I then convinced myself that as > long as I could continue to solve these types of problems, I > would never have difficulty with them in the future. Although > it wasn't absolutely necessary, I successfully attacked a few > more examples just to convince myself that my reasoning was > correct. I haven't had a problem since. > > > Ed Shaughnessy Namely, I could interpret this as the following "theorem": Theorem: I can solve induction problems. (I := author) Proof (by induction): Base case: "I found a book that contained one induction problem that I could solve" Inductive step: "I then convinced myself that as long as I could continue to solve these types of problems, I would never have difficulty with them in the future." Optional further convincing for those not confortable with inductive proofs: "Although it wasn't absolutely necessary, I successfully attacked a few more examples just to convince myself that my reasoning was correct. I haven't had a problem since." Clearly this is not a proof in that the inductive step is unexplained, but the spirit of the reasoning is the same. In either case, this seems a reasonable response to a request for help with inductive proofs. If simple encouragement, it reads like an "I've also been there and survived" comment. If it was intended as an example and parody, it appears to be an artful attempt to be helpful in all three ways (encouragement, example, and parody). Assuming the best, GOOD SHOW! Allen Matsumoto (decvax!ittvax!allenm)