Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site watmath.UUCP
Path: utzoo!watmath!csc
From: csc@watmath.UUCP (Computer Sci Club)
Newsgroups: net.math
Subject: Re: Interesting number proof invalid
Message-ID: <7727@watmath.UUCP>
Date: Fri, 11-May-84 13:43:39 EDT
Article-I.D.: watmath.7727
Posted: Fri May 11 13:43:39 1984
Date-Received: Sat, 12-May-84 10:21:55 EDT
References: <7672@watmath.UUCP> <2457@allegra.UUCP>, <130@westcsr.UUCP>
Organization: U of Waterloo, Ontario
Lines: 20

...

The proof that all numbers are interesting (given the questionable
assumption that the least uninteresting number is interesting) is not
an inductive proof but a proof by contradiction. If we assume the set
of non-interesting numbers is non empty then there is a least non-
interesting number which is by assumption an element of both sets (we
do not remove it from the set of non-interesting numbers, it is already
assumed to be an element of that set) and we have a contradiction.  This
proof is quite valid and very silly.  Note also, although under the normal
ordering of the reals, there exist subsets with no least element, there
exists (if like all right thinking mathematicians you accept the axiom of
choice) an ordering of the reals such that every subset has a least element.
Hence it follows that all real numbers are interesting! 

                                                  William Hughes

DOWN WITH INTUITIONISM!!