From a.rosta@dtn.ntl.com Fri Jul 07 08:42:44 2000 Return-Path: Received: (qmail 5285 invoked from network); 7 Jul 2000 15:42:40 -0000 Received: from unknown (10.1.10.142) by m4.onelist.org with QMQP; 7 Jul 2000 15:42:40 -0000 Received: from unknown (HELO relay3-gui.server.ntli.net) (194.168.4.200) by mta1 with SMTP; 7 Jul 2000 15:42:40 -0000 Received: from m75-mp1-cvx1c.gui.ntl.com ([62.252.12.75] helo=andrew) by relay3-gui.server.ntli.net with smtp (Exim 3.03 #2) id 13Aa7v-00007w-00 for lojban@egroups.com; Fri, 07 Jul 2000 16:33:15 +0100 To: Subject: RE: [lojban] 2 maths questions Date: Fri, 7 Jul 2000 16:42:32 +0100 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook IMO, Build 9.0.2416 (9.0.2910.0) Importance: Normal In-Reply-To: <20000706023805.65157.qmail@hotmail.com> X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 From: "And Rosta" Jorge: > la and cusku di'e > > >2. The set of even numbers and the set of integers are both infinite, > >but how does one express the notion that the latter is bigger, because > >there are twice as many integers as even numbers? > > That erroneous notion can be expressed, for example, as: > > lei relmeina'u lei kacna'u cu xadba le ka kaclai > The even numbers are half the integers in number. Did you realize that I am trying to formulate a statement that is both true and expresses this idea? > >In what property does the set of integers exceed the set of even numbers? > > Apparent numerosity? Something more objective. Jimc mentioned privately that set inclusion might afford a solution, but it wouldn't generalize to say, the way multiples of 2 are more 'numerous' than multiples of 5, but the former don't include the latter. > >I presume > >there is a well-known answer to this question, but the best I can > >do on my own is something along the lines of "frequency" or > >"distributional density" (within the set of integers/numbers/whatever); > > Certainly in any given finite interval (with more than one number > anyway) the integers outnumber the evens, but not in total. > > >if that is the way to go, then how does one actually say it in Lojban? > > lei kacna'u lei relmeina'u cu zmadu le ka denmi Is "denmi" sufficient? Is denmi in the appropriate part of number space a mathematically sensical notion? Can one analogously express the frequency of trains as denmi in time? --And.