From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1319 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Real interval halving Date: Sun, 2 Jan 2000 14:12:30 -0500 (EST) Message-ID: References: <200001012203.OAA16605@coraki.Stanford.EDU> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017747 30703 80.91.229.2 (29 Apr 2009 15:09:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:09:07 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sun Jan 2 16:37:32 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id PAA14044 for categories-list; Sun, 2 Jan 2000 15:40:17 -0400 (AST) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs X-Sender: barr@triples.math.mcgill.ca In-Reply-To: <200001012203.OAA16605@coraki.Stanford.EDU> Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:1319 Archived-At: Perhaps Vaughan is unfamiliar with the following definition of the reals. I got it from Steve Schanuel. I believe that he got it from Serge Lang and he probably got it from Emil Artin. Anyway, Let S be the ring of functions s: N --> N such that the function of two variables (m,n) |--> s(m+n) - s(m) - s(n) is bounded. Addition is element-wise and multiplication is functional composition. Let I consist of the bounded sequences. Then R = S/I. Interestingly, S is not commutative. We now have a real tangent line. Michael