From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4823 Path: news.gmane.org!not-for-mail From: "David Espinosa" Newsgroups: gmane.science.mathematics.categories Subject: Axioms of elementary probability Date: Fri, 8 May 2009 23:02:04 -0700 Message-ID: Reply-To: "David Espinosa" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241878781 28687 80.91.229.12 (9 May 2009 14:19:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 9 May 2009 14:19:41 +0000 (UTC) To: "Categories" Original-X-From: categories@mta.ca Sat May 09 16:19:31 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 1M2nOl-0003e3-4U for gsmc-categories@m.gmane.org; Sat, 09 May 2009 16:19:31 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1M2mgx-00042j-9H for categories-list@mta.ca; Sat, 09 May 2009 10:34:15 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4823 Archived-At: Here's a question about elementary (naive, finitist) probability. The proper, self-dual axioms for elementary probability are presumably P(0) = 0 P(X) = 1 P(A u B) + P(A n B) = P(A) + P(B) P's domain is a boolean algebra. P's codomain is [0,1]. What kind of algebraic structure is [0,1] in this case? What can we prove from this theory? The best I can think of is inclusion / exclusion: P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C) P(A n B n C) = P(A) + P(B) + P(C) - P(A u B) - P(A u C) - P(B u C) + P(A u B u C) Thanks, David