Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: notesfiles Path: utzoo!watmath!clyde!burl!ulysses!mhuxj!houxm!vax135!cornell!uw-beaver!tektronix!hplabs!hp-pcd!hpfclk!fritz 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 LawsAs 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