From cowan@ccil.org Thu Jul 06 10:42:16 2000 Return-Path: Received: (qmail 14432 invoked from network); 6 Jul 2000 17:42:16 -0000 Received: from unknown (10.1.10.27) by m2.onelist.org with QMQP; 6 Jul 2000 17:42:16 -0000 Received: from unknown (HELO locke.ccil.org) (192.190.237.102) by mta1 with SMTP; 6 Jul 2000 17:42:16 -0000 Received: from localhost (cowan@localhost) by locke.ccil.org (8.8.5/8.8.5) with SMTP id OAA16432; Thu, 6 Jul 2000 14:18:17 -0400 (EDT) Date: Thu, 6 Jul 2000 14:18:17 -0400 (EDT) To: And Rosta Cc: lojban Subject: Re: [lojban] 2 maths questions In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-eGroups-From: John Cowan From: John Cowan On Wed, 5 Jul 2000, And Rosta wrote: > 1. How does one say "recurring", as in "0.3 recurring = 0.33333333..."? One says "no pi ra'e ci" = "zero point recurring three". The recurrence mark is placed before the repeating digits, thus eliminating ambiguity about where the repetition starts, as in "ci pi pa vo pa ra'e mu so" = "3.14159595959595..." > 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? In what property > does the set of integers exceed the set of even numbers? 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); I was just wondering about this myself the other day. If there is an answer, it certainly is not commonly taught. In the ordinary mathematics of infinite sets, the set of integers and the set of evens are the same size, because it is possible to construct a one-to-one relation between each member of the two sets (to wit, lambda x 2x). -- John Cowan cowan@ccil.org "You need a change: try Canada" "You need a change: try China" --fortune cookies opened by a couple that I know