From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2126 Path: news.gmane.org!not-for-mail From: Dusko Pavlovic Newsgroups: gmane.science.mathematics.categories Subject: Re: Cauchy completeness of Cauchy reals Date: Fri, 24 Jan 2003 11:48:57 -0800 Message-ID: <3E3198A9.9060902@kestrel.edu> References: <3E31703D.9030801@kestrel.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018430 2612 80.91.229.2 (29 Apr 2009 15:20:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:30 +0000 (UTC) To: CATEGORIES LIST Original-X-From: rrosebru@mta.ca Sat Jan 25 10:50:10 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 25 Jan 2003 10:50:10 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18cR94-0001fi-00 for categories-list@mta.ca; Sat, 25 Jan 2003 10:18:54 -0400 User-Agent: Mozilla/5.0 (X11; U; Linux ppc; en-US; rv:0.9.9) Gecko/20020604 X-Accept-Language: en-us, en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 51 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:2126 Archived-At: heh, i typed this late, and managed to confuse the basic assumption. instead of > let a = (a_i) be a cauchy sequence of rationals between 0 and 1. let a = (a_i) be a cauchy sequence of *cauchy reals*, i.e. each a_i is a cauchy sequence of rationals between 0 and 1. i think the rest goes unchanged: you take a fast converging subsequence b of a, and then approximate b by irredundant rational prefixes. the irredundant representation is thus used instead of choice. the completeness of such representation is the finality of its coalgebraic structure. -- dusko