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From: fritz@hpfclk.UUCP (fritz)
Newsgroups: net.ai
Subject: Re: Inductive Proof - The Heap Problem
Message-ID: <75500005@hpfclk.UUCP>
Date: Sun, 9-Sep-84 13:06:00 EDT
Article-I.D.: hpfclk.75500005
Posted: Sun Sep  9 13:06:00 1984
Date-Received: Wed, 26-Sep-84 03:16:07 EDT
References: <13527@sri-arpa.UUCP>
Organization: Hewlett-Packard - Fort Collins, CO
Lines: 41
Nf-ID: #R:sri-arpa:-1352700:hpfclk:75500005:000:1450
Nf-From: hpfclk!fritz    Sep 18 09:06:00 1984

/***** hpfclk:net.ai / sri-arpa!Laws@SRI-AI.ARPA / 10:14 am  Sep 13, 1984*/
From:  Ken Laws 

As an example of improper induction, consider the heap problem.
A "heap" of one speck (e.g., of flour) is definitely a small heap.
If you add one speck to a small heap, you still have a small heap.
Therefore all heaps are small heaps.

                                        -- Ken Laws
/* ---------- */

That's a little like saying, "The girl next to me is blonde.  The
girl next to her is blonde.  Therefore all girls are blonde."  (Or,
"3 is a prime, 5 is a prime; therefore all odd numbers are prime.")

An observation of 2 (or 3, or 20, or N) samples does *not* an inductive
proof make.  In order to have an inductive proof, you must show that
the observation can be extended to ALL cases.


Mathematician's proof that all odd numbers are prime:
  "3 is a prime, 5 is a prime, 7 is a prime; therefore, by INDUCTION, 
  all odd numbers are prime."

Physicist's proof:
  "3 is a prime, 5 is a prime, 7 is a prime,... uhh, experimental error ...
   11 is a prime, 13 is a prime, ...."

Electrical Engineer's proof:
  "3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime..."

Computer Scientist's proof:
  "3 is a prime, 5 is a prime, 7 is a prime,
			       7 is a prime,
			       7 is a prime,
			       7 is a prime,
			       7 is a prime, ..."
  
Gary Fritz
Hewlett Packard Co
{ihnp4,hplabs}!hpfcla!hpfclk!fritz