From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1366 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Reals a la Eudoxus (updated from re: Tate Reals) Date: Wed, 19 Jan 2000 20:05:27 -0500 (EST) Message-ID: References: <000c01bf622e$0ddd7c60$80213018@buf.adelphia.net> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017778 30901 80.91.229.2 (29 Apr 2009 15:09:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:09:38 +0000 (UTC) Cc: categories@mta.ca, Stephen H Schanuel To: "Stephen H. Schanuel" Original-X-From: rrosebru@mta.ca Wed Jan 19 22:11:46 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id VAA08671 for categories-list; Wed, 19 Jan 2000 21:11:17 -0400 (AST) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs X-Sender: barr@triples.math.mcgill.ca In-Reply-To: <000c01bf622e$0ddd7c60$80213018@buf.adelphia.net> Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 10 Xref: news.gmane.org gmane.science.mathematics.categories:1366 Archived-At: I don't want to be disagreeable, but it seems clear to me that this construction gives Cauchy reals, not Dedekind reals and only the latter can be said to go back to Eudoxus. Indeed, given a nearly function f, with bound B on the near linearity, it is easy to see that |(fn/n) - (fm/m)| =< B(1/n + 1/m) so that the sequence fn/n is Cauchy. Michael