From C.D.Wright@SOLIPSYS.COMPULINK.CO.UK Fri Jul 07 00:54:42 2000 Return-Path: Received: (qmail 3009 invoked from network); 7 Jul 2000 07:54:42 -0000 Received: from unknown (10.1.10.26) by m1.onelist.org with QMQP; 7 Jul 2000 07:54:42 -0000 Received: from unknown (HELO nickel.cix.co.uk) (194.153.0.18) by mta1 with SMTP; 7 Jul 2000 07:54:42 -0000 Received: from s27.pool.pm3-tele-4.cix.co.uk (s27.pool.pm3-tele-4.cix.co.uk [194.153.24.87]) by nickel.cix.co.uk (8.9.3+Sun/8.9.1) with SMTP id IAA24995 for ; Fri, 7 Jul 2000 08:54:39 +0100 (BST) X-Envelope-From: C.D.Wright@solipsys.compulink.co.uk Message-Id: <200007070754.IAA24995@nickel.cix.co.uk> Comments: Authenticated sender is To: lojban Date: Fri, 7 Jul 2000 08:00:20 +0000 Subject: Re: [lojban] 2 maths questions Priority: normal X-mailer: Pegasus Mail for Windows (v2.31) From: C.D.Wright@SOLIPSYS.COMPULINK.CO.UK > I want to able to say that > the set of integers is twice as "thick" ("dense" is already used > for a different property) as the set of evens, and that the set > of evens is 500,000 times as "thick" as the set of multiples of > one million. Given two sets, S1 and S2, S1 is "k-thick" in S2 if for every sequence of intervals (ai,bi) such that bi-ai goes to infinity, the sequence of ratios of the sizes of the intersections between S1 with (ai,bi), and S2 with (ai,bi), has limit k. By this definition the set of primes is 0-thick in the integers, as is the set of powers of two. This is less helpful than you probably want, but generally this sort of definition can be made local. -- \\// ze'uku ko jmive gi'e snada