From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2113 Path: news.gmane.org!not-for-mail From: Dusko Pavlovic Newsgroups: gmane.science.mathematics.categories Subject: Re: Cauchy completeness of Cauchy reals Date: Wed, 22 Jan 2003 15:33:00 -0800 Message-ID: References: <15918.28389.594290.761117@acws-0054.cs.bham.ac.uk> 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 1241018419 2544 80.91.229.2 (29 Apr 2009 15:20:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:19 +0000 (UTC) To: CATEGORIES LIST Original-X-From: rrosebru@mta.ca Thu Jan 23 13:27:04 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 23 Jan 2003 13:27:04 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18bl2K-00044A-00 for categories-list@mta.ca; Thu, 23 Jan 2003 13:21:08 -0400 User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.1) Gecko/20021003 X-Accept-Language: en-us, en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 38 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:2113 Archived-At: Martin Escardo wrote: >NB. Freyd characterized the Dedekind reals as a final coalgebra. Alex >Simpson and I characterized "the Cauchy completion of the rationals >within the Dedekind reals" as a free algebra > and vaughan pratt and i characterized the cauchy reals as a final coalgebra. the papers are i proceedings of CMCS 99 and in TCS 280. in fact, freyd came up with his characterization of the closed interval while commenting on our first paper, where vaughan and i worked with the semiopen interval. but it is fair to say that the algebraic approach allows easier algebraic operations on reals. (i only managed to multiply them in one of our coalgebras, and in a very inefficient way.) -- dusko BTW have you seen the book: Life Itself. A Comprehensive Inquiry Into the Nature, Origin, and Fabrication of Life by Robert Rosen (Columbia University Press 1991) it was referenced in a biology paper, i found it in the biology library, and it's full of categories. (yes, i kno, people often do that to sound complicated, but this seems like honest work, perhaps even inspiring, although it does not go very deep.)