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Path: utzoo!watmath!csc
From: csc@watmath.UUCP (Computer Sci Club)
Newsgroups: net.math
Subject: Re: Interesting Numbers
Message-ID: <7715@watmath.UUCP>
Date: Thu, 10-May-84 21:45:48 EDT
Article-I.D.: watmath.7715
Posted: Thu May 10 21:45:48 1984
Date-Received: Sat, 12-May-84 08:46:20 EDT
References: <1279@uvacs.UUCP>, <1517@brl-vgr.ARPA>
Organization: U of Waterloo, Ontario
Lines: 23

...

Problem find sets A and B such that:

              (i) A union B = positive integers
             (ii) A intesect B = the empty set
            (iii) If B has a least element then this element is an element of A

Solution A= positive integers, B= empty set

 Proof  Assume B non-empty, then B has a least element, therefore
        by (iii) A intersect B is non-empty contradicting (ii).
        Therefore B is empty, therefore by (i) A= positive integers.

   Now call A interesting numbers and B non-interesting numbers and
we have a proof that there are no non-interesting numbers. (given
(i),(ii), and (iii) which as has been pointed out may not be very
reasonable)  I do not see any problem with the above formulation.
(in particular it is not equivalent to the unexpected hanging date
paradox)
                              William Hughes