From thorild@UPDATE.UU.SE Thu Jul 06 15:37:11 2000 Return-Path: Received: (qmail 7981 invoked from network); 6 Jul 2000 22:37:10 -0000 Received: from unknown (10.1.10.26) by m4.onelist.org with QMQP; 6 Jul 2000 22:37:10 -0000 Received: from unknown (HELO Zeke.Update.UU.SE) (130.238.11.14) by mta1 with SMTP; 6 Jul 2000 22:37:10 -0000 Received: (from thorild@localhost) by Zeke.Update.UU.SE (8.8.8/8.8.8) id AAA27948; Fri, 7 Jul 2000 00:37:08 +0200 Date: Fri, 7 Jul 2000 00:37:08 +0200 Message-Id: <200007062237.AAA27948@Zeke.Update.UU.SE> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit To: lojban Subject: Re: [lojban] 2 maths questions In-Reply-To: References: X-Mailer: VM 6.34 under Emacs 20.2.2 From: Thorild Selen X-Yahoo-Message-Num: 3442 John Cowan writes: > On Wed, 5 Jul 2000, And Rosta wrote: > > but how does one express the notion that the latter is bigger, because > > there are twice as many integers as even numbers? In what property > > does the set of integers exceed the set of even numbers? [...] > > I was just wondering about this myself the other day. If there is an > answer, it certainly is not commonly taught. [...] Aren't you trying to make things a little too complicated here? What you really want to say is probably that the set of even numbers is a _proper subset_ of the set of integers, so there is certainly a well known name for this relation. Naming the property in which one of the sets exceeds the other may be a bit trickier. Maybe one could call it "the property of containing much" (that sounds like size, but, as John said, the two sets are of the same size, so we can't call the property "size" unless we really want to cause confusion). The relations "larger" and "smaller" on this property should be the superset and subset relations (thus not a total ordering). Using a "frequency" property to compare these sets was also mentioned. The idea is probably that the the number of integers in the range [0,n] that are in the first set is larger than the number of integers within the same interval that are in the second set, and that this holds for arbitrarily large values of n. I can't come up with a better name for this property, but if you need to talk about it, it would probably be wise to start by declaring a name for it. /Thorild