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From: ags@pucc-h (Dave Seaman)
Newsgroups: net.puzzle,net.math
Subject: Re: Infinite random-number generators
Message-ID: <2455@pucc-h>
Date: Sun, 17-Nov-85 12:53:06 EST
Article-I.D.: pucc-h.2455
Posted: Sun Nov 17 12:53:06 1985
Date-Received: Tue, 19-Nov-85 03:21:51 EST
References: <1635@decwrl.UUCP> <787@mhuxt.UUCP> <321@mmm.UUCP>
Reply-To: ags@pucc-h.UUCP (Dave Seaman)
Organization: Purdue University Computing Center
Lines: 26
Xref: watmath net.puzzle:1176 net.math:2533

In article <321@mmm.UUCP> cipher@mmm.UUCP (Andre Guirard) writes:
>In article <787@mhuxt.UUCP> js2j@mhuxt.UUCP (sonntag) writes:
>>> 	This isn't quite the answer yet.  For one thing, I doubt it's
>>> 	uniformly distributed.  Also, this answer is from 0 to infinity, and
>>> 	I'm looking for negative infinity to positive infinity.
>>
>>    Now he tells us that it's got to be uniformly distributed?  If such
>>a function exists, the probability of it generating a number between any
>>two arbitrarily large, but finite limits is exactly 0!  Why would
>					     ^^^^^^^^^
>>anyone want a random number generator like that?
>
>Not zero, since the random number generator will in fact come up with a
>number.  The chances are infinitesimal.  The difference is admittedly
>very subtle.

To say that an event has probability zero does not mean the event is impossible.
Anle.
Analogously, to say that a set has measure zero does not mean the set is empty.
The Cantor set has uncountably many points in it, but its measure is zero.
A uniformly-distributed random variable on the unit interval has probability
zero of being in the Cantor set, though such an event is obviously possible.

There is no such thing as an infinitesimal probability.
-- 
Dave Seaman			 ..!pur-ee!pucc-h!ags