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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
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Organization: ITT-ATC, Stratford Ct.
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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)