From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.org!.POSTED!not-for-mail From: "Herring, Davis" Newsgroups: gmane.emacs.devel Subject: Re: Making 'eq' == 'eql' in bignum branch Date: Sat, 1 Sep 2018 01:05:33 +0000 Message-ID: <0fdc8b299a614b07b4aa437993a976bd@lanl.gov> References: <0F8F6E54-176C-48EE-9E7C-7CAC424D0D55@raeburn.org> <352c998a64c646b983a131039e9c732b@lanl.gov>, <20180831195942.GA4898@ACM> NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1535764661 28424 195.159.176.226 (1 Sep 2018 01:17:41 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 1 Sep 2018 01:17:41 +0000 (UTC) Cc: "cpitclaudel@gmail.com" , Pip Cet , "emacs-devel@gnu.org" To: Alan Mackenzie Original-X-From: emacs-devel-bounces+ged-emacs-devel=m.gmane.org@gnu.org Sat Sep 01 03:17:36 2018 Return-path: Envelope-to: ged-emacs-devel@m.gmane.org Original-Received: from lists.gnu.org ([208.118.235.17]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1fvuXg-0007Is-9M for ged-emacs-devel@m.gmane.org; Sat, 01 Sep 2018 03:17:36 +0200 Original-Received: from localhost ([::1]:59089 helo=lists.gnu.org) by lists.gnu.org with esmtp (Exim 4.71) (envelope-from ) id 1fvuZm-0006DG-Le for ged-emacs-devel@m.gmane.org; Fri, 31 Aug 2018 21:19:46 -0400 Original-Received: from eggs.gnu.org ([2001:4830:134:3::10]:55501) by lists.gnu.org with esmtp (Exim 4.71) (envelope-from ) id 1fvuZ2-0006BV-1c for emacs-devel@gnu.org; Fri, 31 Aug 2018 21:19:04 -0400 Original-Received: from Debian-exim by eggs.gnu.org with spam-scanned (Exim 4.71) (envelope-from ) id 1fvuN5-0005we-Ey for emacs-devel@gnu.org; Fri, 31 Aug 2018 21:06:44 -0400 Original-Received: from proofpoint8.lanl.gov ([204.121.3.47]:44670) by eggs.gnu.org with esmtps (TLS1.0:RSA_AES_256_CBC_SHA1:32) (Exim 4.71) (envelope-from ) id 1fvuN5-0005ux-5F for emacs-devel@gnu.org; Fri, 31 Aug 2018 21:06:39 -0400 Original-Received: from pps.filterd (proofpoint8.lanl.gov [127.0.0.1]) by proofpoint8.lanl.gov (8.16.0.22/8.16.0.22) with SMTP id w8111d7I036132; Fri, 31 Aug 2018 19:05:34 -0600 DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=lanl.gov; h=from : to : cc : subject : date : message-id : references : in-reply-to : content-type : content-transfer-encoding : mime-version; s=lanl; bh=Gi397u4gkmn95YLtVc4yoTXHXct972brwr0cecQpJEk=; b=HqP+jFhLAjdIfKMW9k3ruLCBbIlzvNdsPv1G+v3WG+MdH8w5Prv9oNo4Dh/zw4wAOzEp TPTEZs1IkBZizjGTBB1OySGtdzrr2vQFezN8rEb/hbKlci98cQ/VBWQwppa4s+jn+xxd NitU77FK0PXRcA+EFaizXpwLAAYDJteN/aIZIjh7l0thBkd5wM6GXnM3/ezTRaate8oj 36gW3E1gaCr6nDtv1NOVEgzL4vHL9ArgldJ4px6chs7yteRwm9ftNN8tvMoLTUptQ+i+ MjZ9JpKfWFplaAf7JIotBdBzULrtOpP2+n9Rb3iDr/0FOCAAPTo6trxDcfv+A8xVN85v Dg== Original-Received: from mailrelay2.lanl.gov (mailrelay2.lanl.gov [128.165.4.103]) by proofpoint8.lanl.gov with ESMTP id 2m33w1j3be-1; Fri, 31 Aug 2018 19:05:34 -0600 Original-Received: from localhost (localhost.localdomain [127.0.0.1]) by mailrelay2.lanl.gov (Postfix) with ESMTP id 0AE49F075D4; Fri, 31 Aug 2018 19:05:34 -0600 (MDT) X-NIE-2-Virus-Scanner: amavisd-new at mailrelay2.lanl.gov Original-Received: from EXG16-P-MBX06.win.lanl.gov (exg16-p-mbx06.win.lanl.gov [128.165.106.186]) by mailrelay2.lanl.gov (Postfix) with ESMTP id DEC26F075D2; Fri, 31 Aug 2018 19:05:33 -0600 (MDT) Original-Received: from EXG16-P-MBX03.win.lanl.gov (128.165.106.183) by EXG16-P-MBX06.win.lanl.gov (128.165.106.186) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.1.1531.3; Fri, 31 Aug 2018 19:05:33 -0600 Original-Received: from EXG16-P-MBX03.win.lanl.gov ([fe80::7c23:7a54:2544:a5c4]) by EXG16-P-MBX03.win.lanl.gov ([fe80::7c23:7a54:2544:a5c4%2]) with mapi id 15.01.1531.004; Fri, 31 Aug 2018 19:05:33 -0600 Thread-Topic: Making 'eq' == 'eql' in bignum branch Thread-Index: AQHUJe8LD6NzhSV8GEm1qwYJaFkj56SksmolgAFAbQCAIfRMJoAA0Z4AgAAIcQCAAAPVgIAAIEK+gAADi2yAAM3mKIAH+FMAgAEBu7WAAHsOgIABayq8gABucgCAAFZngP//6vOlgADD7ACAAFMVAP//5p7EgASenAD//+YSCQ== In-Reply-To: <20180831195942.GA4898@ACM> Accept-Language: en-US Content-Language: en-US X-MS-Has-Attach: X-MS-TNEF-Correlator: x-originating-ip: [128.165.106.203] X-Proofpoint-Virus-Version: vendor=fsecure engine=2.50.10434:, , definitions=2018-08-31_11:, , signatures=0 X-Proofpoint-Spam-Details: rule=notspam policy=default score=0 priorityscore=1501 malwarescore=0 suspectscore=0 phishscore=0 bulkscore=0 spamscore=0 clxscore=1011 lowpriorityscore=0 mlxscore=0 impostorscore=0 mlxlogscore=999 adultscore=0 classifier=spam adjust=0 reason=mlx scancount=1 engine=8.0.1-1807170000 definitions=main-1809010009 X-detected-operating-system: by eggs.gnu.org: GNU/Linux 3.x [generic] [fuzzy] X-Received-From: 204.121.3.47 X-BeenThere: emacs-devel@gnu.org X-Mailman-Version: 2.1.21 Precedence: list List-Id: "Emacs development discussions." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: emacs-devel-bounces+ged-emacs-devel=m.gmane.org@gnu.org Original-Sender: "Emacs-devel" Xref: news.gmane.org gmane.emacs.devel:229152 Archived-At: > +/-infinity are not numbers. They do not satisfy the axioms which > define numbers. For example they do not satisfy >=20 > (x + y) + z =3D x + (y + z) What is the list of such axioms? If it includes the existence of an additi= ve identity, you lose the natural numbers; if it includes the trichotomy pr= operty, you lose the complex numbers; if it includes commutativity of addit= ion, you lose the ordinal numbers. Of course we can decide that any or all= of those "aren't really numbers", but why? While addition is one of the operations with the broadest applicability (bu= t see the supernatural numbers) and associativity is one of the properties = most widely required of a binary operation (but see the octonions), even as= sociativity of addition is sometimes violated (consider the example of infi= nite series ). >> They're not real numbers, but neither are complex numbers, >> split-complex numbers, dual numbers, p-adic numbers, quaternions, >> octonions, sedenions, hyperreal numbers, or (please no) surreal >> numbers. >=20 > That's a strawman. The issue being discussed here is numbers, not > arbitrary algebraic structures. Which of those sets aren't sets of numbers? No one said anything about vec= tor spaces, Lie groups, Sobolev spaces, tangent bundles, etc. >> With all due respect to your mathematician friend, .... >=20 > That is offensive in the extreme. I'm sorry, but I don't understand how. I _meant_ the "due respect" that I = wrote. Perhaps I should not presume that any two people are friends, but t= he broad use of that term was meant to be generous, not condescending. >> .... she has no exclusive claim over the definition (such as it is) of >> "number" >=20 > That's analagous to saying that climate scientists don't have the > exclusive say-so about climate change. Ha ha, who needs experts? I don't follow the analogy. Outside of trivial misconceptions (like "weath= er" vs. "climate"), I don't know of a situation where the _definition_ of "= climate change" is unclear. On the other hand, I don't know of any rigorou= s definition for "number" (thus my request for axioms above). > I would have expected, > in this mailing list (as contrasted with lesser forums) to see respect > for expertise, not disparagement. No one is disparaging expertise, certainly not in general. Experts routine= ly disagree, without any disrespect, about the more philosophical topics in= their field. Given (what I consider to be) such a weakness of definition,= I remain uncertain why a mathematical expert would so flatly reject a wide= ly-used category of "number". >> (and I'm a bit surprised if she hadn't heard of at least one of the >> extended real lines I linked). >=20 > Again, offensive. Again, I'm afraid you'll have to explain. I stated that I considered it un= likely that a mathematician would be unfamiliar with the extended reals (co= nsidering that they are used as a notational device even in Calculus I). I= said so because I don't know what other explanation to offer for such surp= rise at the IEEE rules, based so closely as they are on the extended reals. Davis=