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From: ecn-ec:ecn-pc:ecn-ed:vu@pur-ee.UUCP
Newsgroups: net.math
Subject: Re: A new paradox?
Message-ID: <204@ecn-ed.UUCP>
Date: Thu, 15-Sep-83 16:52:28 EDT
Article-I.D.: ecn-ed.204
Posted: Thu Sep 15 16:52:28 1983
Date-Received: Sat, 17-Sep-83 05:46:54 EDT
References: 5941ux.406
Lines: 17


	(And yet another dummy)

That "paradox" is rather old and well-known. The fallacy lies in the fact
that induction does not apply to all sets. Take your set of n-1 elements.
Which one is x(1) ? How did you pick it ? You say "pick any of them" ?
No: the choice must be objective (Try to program a computer to pick an
number, any number, from a set of data !! If you use random number,
the computer is not picking A number, it is picking THE number that
conforms somehow to the random number it generated). In fact, principle
of inductions applies for a set N if and only if N has a smallest
element, whereas "smallest" doesn't necessarily means numerically
smallest. If you can somehow OBJECTIVELY define an order in your set
of n-1 element, then induction will apply. But you can't. So induction
doesn't apply.

Hao-Nhien Vu (pur-ee!norris)