source file: mills2.txt Date: Tue, 19 Dec 1995 21:05:36 -0800 Subject: Re: TUNING digest 589 From: Mmcky@aol.com Brian Writes: >...but belief is *not* the same thing as proof... Actually, there are those of us who believe that proof and belief are exactly the same thing. Others don't believe in believing, and view "proof" as a somewhat underhanded means of persuasion. >To my >knowledge, there is as yet no known algorithm >by which the entire field of reals may be sieved >and by which all transcendental numbers will >always be found. There may be no such thing as a transcendental number. A number cannot be recognized as transcendental, or even irrational, by the mere quoting of digits, because no matter how many digits are enumerated, one can never be sure that specifying more digits will not result in a repetition, and thus reduce the number to a mere rational. Therefore, we do not have a transcendental, number, but a transcendental algorithm. No possible enumeration of a subset of the digits can allow us to determine whether the number is even rational or not, much less distinguish the transcendentals from the irrationals. An analysis of the generating algorithm may give an indication. I think that for the purposes of this forum, there is no practical difference between transcendental numbers, irrationals, and large irreducible rationals. Anything that goes beyond the resolution of the ear is off the scale as far as tuning is concerned. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 20 Dec 1995 10:38 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id BAA10138; Wed, 20 Dec 1995 01:37:38 -0800 Date: Wed, 20 Dec 1995 01:37:38 -0800 Message-Id: <0099B24F6BF12512.4F84@ezh.nl> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu