From jjllambias@hotmail.com Fri Jul 07 16:54:18 2000 Return-Path: Received: (qmail 10652 invoked from network); 7 Jul 2000 23:54:15 -0000 Received: from unknown (10.1.10.26) by m3.onelist.org with QMQP; 7 Jul 2000 23:54:15 -0000 Received: from unknown (HELO hotmail.com) (216.33.240.138) by mta1 with SMTP; 7 Jul 2000 23:54:15 -0000 Received: (qmail 61691 invoked by uid 0); 7 Jul 2000 23:54:14 -0000 Message-ID: <20000707235414.61690.qmail@hotmail.com> Received: from 200.42.154.168 by www.hotmail.com with HTTP; Fri, 07 Jul 2000 16:54:14 PDT X-Originating-IP: [200.42.154.168] To: lojban@egroups.com Subject: RE: [lojban] 2 maths questions Date: Fri, 07 Jul 2000 16:54:14 PDT Mime-Version: 1.0 Content-Type: text/plain; format=flowed From: "Jorge Llambias" la and cusku di'e > > >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? If you want to make a mathematical statement, the idea is just wrong, there are not twice as many integers as even numbers in the usual mathematical sense. It is of course possible to define some new mathematical function that assigns to the integers twice the value that it assigns the even numbers (the function proposed taking limits is probably the best), but what do we want it for? > > lei kacna'u lei relmeina'u cu zmadu le ka denmi > >Is "denmi" sufficient? It has been pointed out that "dense" is already used for something else in maths. For example, the set of rationals is dense in the set of reals. Even though an interval of rationals is full of holes, any real interval contains rationals. The integers are not dense because you can find intervals where there are no integers (for example between 0.2 and 0.5). {denmi} does not necessarily mean this yet, but it is reasonable to expect that Lojbanist mathematicians will want to use it with that sense. >Is denmi in the appropriate part of number space a >mathematically sensical notion? Not until someone defines it. But then why not? >Can one analogously express the frequency >of trains as denmi in time? It seems possible. x3 would have to be the time interval. co'o mi'e xorxes ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com