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From: mdr@bentley.UUCP (M. Rossner)
Newsgroups: net.puzzle
Subject: Re: truth machine clarification**2
Message-ID: <616@bentley.UUCP>
Date: Fri, 7-Mar-86 13:40:36 EST
Article-I.D.: bentley.616
Posted: Fri Mar  7 13:40:36 1986
Date-Received: Sun, 9-Mar-86 00:32:53 EST
References: <423@watdragon.UUCP> <2664@pucc-h> <394@link.UUCP>, <2109@jhunix.UUCP>
Organization: AT&T Bell Laboratories, Liberty Corner
Lines: 19


>You mean countable.  If the set is countable there exists a 1 to 1
>correspondence with the set of positive integers.  Thus each true
>statement can be associated with a unique integer.  We need only
>specify that the machine produces the statements in this order to
>guarantee that any true statement is eventually produced.


And it is obvious that the set of true sentences is countabe.  I need
only concatenate together the ASCII codes for each character in the
sentence to come up with a unique positive integer for that sentence.
If the sentences are identical, the integers will be identical; if the
integers are identical, the sentences must have been the same.  Thus the
number of sentences (not even necessarily true) is countably infinite,
as is the number of computer programs, books, musical scores (using 
Western notation), or any other printed matter.

                   Marc D. Rossner
                   AT&T Bell Labs, Liberty Corner