Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.PCS 1/10/84; site mtgzz.UUCP
Path: utzoo!watmath!clyde!cbosgd!ihnp4!mhuxn!mhuxr!mhuxt!houxm!mtuxo!mtgzz!leeper
From: leeper@mtgzz.UUCP (m.r.leeper)
Newsgroups: net.puzzle
Subject: Re: random number wanted between neg inf and pos inf
Message-ID: <1505@mtgzz.UUCP>
Date: Sat, 21-Dec-85 16:13:11 EST
Article-I.D.: mtgzz.1505
Posted: Sat Dec 21 16:13:11 1985
Date-Received: Mon, 23-Dec-85 04:19:28 EST
References: <33@decwrl.UUCP> <797@brl-tgr.ARPA>
Organization: AT&T Information Systems Labs, Middletown NJ
Lines: 32

> > I'm the original poser of the problem.  I'm surprised at the high
> > smart-ass/serious ratio on the responses.
> 
> Anyone who asks for a generator of random numbers
> uniformly distributed from -Infinity to +Infinity
> deserves what he gets.

Well someone should explain why it is impossible to have a uniform
distribution on a set of infinite measure.  One way to look at it is
that the highest number that any program on a real computer could give
you would be just too near to zero to be a realistic choice for the
random number generator you ask for.   Assume you have a uniform
distribution on -inf to +inf.   Let M be the largest finite number the
human mind has ever conceived.  The interval from -M to M is of finite
measure, that implies that the probability of the number picked at 
random (uniformly distributed on -inf to +inf) falling into this
interval is zero!  Certainly most (and that is putting it lightly) of
the numbers generated would fall outside of this interval.  That is
not a rigorous proof that you cannot uniformly distribute on a set of
infinite measure, but it should give you some idea that it would not
do you any good even if you could.

All numbers are small in magnitude.  On the real number line, the
human mind can conceive of only those numbers extremely close to zero,
so close to zero that if you were picking a real number at random
(uniformly distributed) the probability is zero that you would pick a
numbers with so small an absolute value.  We can conceive of the
boundries of the real number line and a tiny island of numbers in a
tiny neighborhood around zero.

				Mark Leeper
				...ihnp4!mtgzz!leeper