Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10 5/3/83; site cvl.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!ittvax!dcdwest!sdcsvax!sdcrdcf!hplabs!hao!seismo!rlgvax!cvl!rlh
From: rlh@cvl.UUCP
Newsgroups: net.math
Subject: Interesting Numbers
Message-ID: <975@cvl.UUCP>
Date: Mon, 7-May-84 07:26:47 EDT
Article-I.D.: cvl.975
Posted: Mon May  7 07:26:47 1984
Date-Received: Fri, 11-May-84 07:24:10 EDT
Organization: U. of Md. Computer Vision Lab
Lines: 30


    'Interesting Assumption':
    Assume that for any property P (or any property in a class which
    contains the properties used below), if x is the least positive
    integer with property P, then x is interesting.  Also assume that
    no positive integer x is both interesting and uninteresting.

Are you kidding? With this assumption there is a much shorter "proof".
Any number n is interesting because it is the least positive integer
with the property of being greater than n-1. This is absurd. Not all
properties are interesting.

The proof by induction used to prove all numbers are interesting is
similar to the proof of the hang-man paradox.  A prisoner is told that
he will be hanged by friday and will not know the day on which he is to
be hanged.  He cant be hanged on friday because if he survived
past thursday he would know the day of his hanging.  But then thursday
is the last possible day and can be eliminated by a similar argument.  By
induction he can prove that he can`t be hanged at all without knowing
the day.  (However, the hangman comes unexpectedly on wednesday.)

The real error is the assumption that there is a set of numbers that
are intrinsically interesting. In reality there is only the set of of
numbers that a particular person is interested in at a particular time.
One can`t be interested in the smallest number in which one is not
interested. (If you are then you aren`t because it dosn`t exist)

			Ralph Hartley
			rlh@cvl.arpa
			seismo!rlgvax!cvl!rlh   ?