From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1575 Path: news.gmane.org!not-for-mail From: "Osher Doctorow" Newsgroups: gmane.science.mathematics.categories Subject: Re: Cross-Category "conversions" of some interest Date: Wed, 19 Jul 2000 19:15:38 -0700 Message-ID: <001e01bff1f0$877ca080$1e7379a5@osherphd> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_001B_01BFF1B5.B93B2960" X-Trace: ger.gmane.org 1241017936 31889 80.91.229.2 (29 Apr 2009 15:12:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:12:16 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Tue Jul 25 10:08:55 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA00526 for categories-list; Tue, 25 Jul 2000 10:02:18 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 17 Original-Lines: 149 Xref: news.gmane.org gmane.science.mathematics.categories:1575 Archived-At: This is a multi-part message in MIME format. ------=_NextPart_000_001B_01BFF1B5.B93B2960 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable From: Osher Doctorow osher@ix.netcom.com, Wed. July 19, 2000, 7:04PM A list member claims in a private communication to me that 3 things are = wrong with the x/y to 1 - x + y conversion. His first claim is that "it = does not ring true" that I meant to type k1 or k2. This criticism is = outside mathematics and has no meaning either there or in science. His second claim is that xy =3D (x/y)y^^2 works one way and (x/y)^^2 = (y^^3)/x works another way in the conversion and that the conversion of = / but not other operations is anyway of questionable validity. = Concerning the second part, the claim is meaningless. Since x/y is the = main "animal" in BCP and in Goguen/Product logic implication and both = have the form x/y, there is nothing to prevent me from comparing x/y = with 1 - x + y in order to compare BCP and Goguen/Product logic = implications with LBP and Lukaciewicz Logic. Concerning the first part, = we can define a conversion C_n which converts xy as a product of = (x/y)^^n g(x,y) where g(x,y) is a rational expression in powers of y = and/or x no part of which contains (x/y)^^m as a factor for 1 < =3D m < = =3D n and m, n are integers > =3D 1. C_n (C subscript n) for n =3D 1 = gives exactly my conversion, and the critic's objection case involves = C_2 which conversion is not being considered. The third argument is that the conversion restricted to x/y for x, y = coprime integers is alarming (because) continuity is lost (that is to = say, I should mention, that the rationals are not continuous while the = reals are) and because it is unclear how to apply the conversion to = expressions of the form xy (is xy to be the product of two coprime = integers or what?). This is really two objections except for the word = "alarming" which is not a word in mathematics or science. The first = objection, concerning continuity, implicitly assumes that the conversion = is required to be continuous. Although I used the conversion earlier to = attempt to convert xy in the Heisenberg Uncertainty Principle (HUP) xy > = k, which perhaps should "ideally" involve all real xy, if the critic = admits that the conversion works for rational x and y or even integer x = and y, then xy restricted to either rational or integer x and y converts = to two different inequalities depending on whether 1 - x + y < 0 or 1 - = x + y > 0 (respectively x > 1 + y or x < 1 + y), so the converted form = of xy does not obey the HUP, and therefore continuity is not even = required to show what I had attempted to show about the HUP. The second = objection, concerning whether xy is restricted to the product of two = coprime integers, is rather redundant considering the above. Yours truly, Osher Doctorow=20 ------=_NextPart_000_001B_01BFF1B5.B93B2960 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
From: Osher Doctorow osher@ix.netcom.com, Wed. July = 19, 2000,=20 7:04PM
 

I am sending this again because of I typed "real" instead of = "integer" in one=20 place.

A list member claims in a private communication to me that 3 things = are wrong=20 with the x/y to 1 - x + y conversion. His first claim is that "it does = not ring=20 true" that I meant to type k1 or k2. This criticism is outside = mathematics and=20 has no meaning either there or in science.

His second claim is that xy =3D (x/y)y^^2 works one way and (x/y)^^2 = (y^^3)/x=20 works another way in the conversion and that the conversion of / but not = other=20 operations is anyway of questionable validity. Concerning the second = part, the=20 claim is meaningless. Since x/y is the main "animal" in BCP and in=20 Goguen/Product logic implication and both have the form x/y, there is = nothing to=20 prevent me from comparing x/y with 1 - x + y in order to compare BCP and = Goguen/Product logic implications with LBP and Lukaciewicz Logic. = Concerning the=20 first part, we can define a conversion C_n which converts xy as a = product of=20 (x/y)^^n g(x,y) where g(x,y) is a rational expression in powers of y = and/or x no=20 part of which contains (x/y)^^m as a factor for 1 < =3D m < =3D n = and m, n are=20 integers > =3D 1. C_n (C subscript n) for n =3D 1 gives exactly my = conversion,=20 and the critic’s objection case involves C_2 which conversion is = not being=20 considered.

The third argument is that the conversion restricted to x/y for x, y = coprime=20 integers is alarming (because) continuity is lost (that is to say, I = should=20 mention, that the rationals are not continuous while the reals are) and = because=20 it is unclear how to apply the conversion to expressions of the form xy = (is xy=20 to be the product of two coprime integers or what?). This is really two=20 objections except for the word "alarming" which is not a word in = mathematics or=20 science. The first objection, concerning continuity, implicitly assumes = that the=20 conversion is required to be continuous. Although I used the conversion = earlier=20 to attempt to convert xy in the Heisenberg Uncertainty Principle (HUP) = xy >=20 k, which perhaps should "ideally" involve all real xy, if the critic = admits that=20 the conversion works for rational x and y or even integer x and y, then = xy=20 restricted to either rational or integer x and y converts to two = different=20 inequalities depending on whether 1 - x + y < 0 or 1 - x + y > 0=20 (respectively x > 1 + y or x < 1 + y), so the converted form of xy = does=20 not obey the HUP, and therefore continuity is not even required to show = what I=20 had attempted to show about the HUP. The second objection, concerning = whether xy=20 is restricted to the product of two coprime integers, is rather = redundant=20 considering the above.

Yours truly,

Osher Doctorow

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