From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/29 Path: news.gmane.org!not-for-mail From: "Galchin, Vasili" Newsgroups: gmane.science.mathematics.categories Subject: Re: "Kantor dust" Date: Fri, 30 Jan 2009 22:35:41 -0600 Message-ID: Reply-To: "Galchin, Vasili" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1233411543 22723 80.91.229.12 (31 Jan 2009 14:19:03 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 31 Jan 2009 14:19:03 +0000 (UTC) To: Bas Spitters Original-X-From: categories@mta.ca Sat Jan 31 15:20:17 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 1LTGhg-0007Me-4K for gsmc-categories@m.gmane.org; Sat, 31 Jan 2009 15:20:12 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG7G-0006Lh-8r for categories-list@mta.ca; Sat, 31 Jan 2009 09:42:34 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:29 Archived-At: i.e. a well-defined algorithm exists to construct Cantor dust but the Cantor dust cannot be constructed/built from the algorithm in a finite number of steps. Hence, Cantor dust represents potential infinity rather than actual infinity. This problem has nagged at me for a while. Regards, Vasili On Fri, Jan 30, 2009 at 4:40 PM, Galchin, Vasili wrote: > I don't think it exists from a constructivist viewpoint because it has to > be constructed in a finite number of steps. > > Vasili > > On Fri, Jan 30, 2009 at 3:52 PM, Bas Spitters wrote: > >> On Friday 30 January 2009 08:18:39 Galchin, Vasili wrote: >> > Here is a definition of Cantor dust .... >> > http://en.wikipedia.org/wiki/Cantor_set. >> > >> > My question is from a constructivist viewpoint does this set >> really >> > exist and if so, why? >> >> Yes, it exists. In fact, it is a continuous image of 2^N. >> It is Bishop compact, fan-like and compact overt (choose your taste of >> constructivism). >> >> Bas >> >> >