From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/50 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: "Kantor dust" Date: Sun, 8 Feb 2009 14:51:19 +0000 (GMT) Message-ID: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1234127736 746 80.91.229.12 (8 Feb 2009 21:15:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 8 Feb 2009 21:15:36 +0000 (UTC) To: Toby Bartels , Original-X-From: categories@mta.ca Sun Feb 08 22:16:50 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LWH1C-0001Zd-SD for gsmc-categories@m.gmane.org; Sun, 08 Feb 2009 22:16:47 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LWGQH-0002oB-Qf for categories-list@mta.ca; Sun, 08 Feb 2009 16:38:37 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:50 Archived-At: On Sat, 7 Feb 2009, Toby Bartels wrote: >> Toby was of course referring to the Dedekind reals > > Actually, I was trying to keep it open, > since different schools of constructivism have different opinions > about which are the correct reals (as well as which are equivalent). > But nobody uses the binary reals, since they can't subtract them. Never mind subtraction -- you can't even add them. As I mentioned in my last posting, the question "Is x < 1/2?" is decidable for Vaughan's binary reals, but "Is x < 1/3?" is not (constructively), so the operation of adding 1/6 can't be defined. Peter Johnstone