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From: leimkuhl@uiuccsb.UUCP
Newsgroups: net.math
Subject: Re: A new paradox? - (nf)
Message-ID: <2831@uiucdcs.UUCP>
Date: Thu, 15-Sep-83 22:33:55 EDT
Article-I.D.: uiucdcs.2831
Posted: Thu Sep 15 22:33:55 1983
Date-Received: Sat, 17-Sep-83 06:03:13 EDT
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#R:5941ux:-40600:uiuccsb:9700006:000:355
uiuccsb!leimkuhl    Sep 15 21:38:00 1983


The problem lies in your assumption that n=1 is adequate "base case."

Mathematical induction defined:
  If P1 and Pn-1 => Pn (for n=2,3...) then Pn (for n=1,2...)

In this case Pn is the statement "any n numbers are equal."  And the problem
is that your induction step implicitly assumes n>2 so that P1=>P2 is never
checked (and of course, this fails).