From lojban-out@lojban.org Mon Jan 27 15:29:40 2003 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_2_3_0); 27 Jan 2003 23:29:40 -0000 Received: (qmail 31689 invoked from network); 27 Jan 2003 23:29:40 -0000 Received: from unknown (66.218.66.217) by m14.grp.scd.yahoo.com with QMQP; 27 Jan 2003 23:29:40 -0000 Received: from unknown (HELO digitalkingdom.org) (204.152.186.175) by mta2.grp.scd.yahoo.com with SMTP; 27 Jan 2003 23:29:40 -0000 Received: from lojban-out by digitalkingdom.org with local (Exim 4.05) id 18dIhA-0006QV-00 for lojban@yahoogroups.com; Mon, 27 Jan 2003 15:29:40 -0800 Received: from digitalkingdom.org ([204.152.186.175] helo=chain) by digitalkingdom.org with esmtp (Exim 4.05) id 18dIgu-0006QA-00; Mon, 27 Jan 2003 15:29:24 -0800 Received: with ECARTIS (v1.0.0; list lojban-list); Mon, 27 Jan 2003 15:29:23 -0800 (PST) Received: from dhc112.chch.ox.ac.uk ([163.1.237.112] helo=dave ident=0) by digitalkingdom.org with esmtp (Exim 4.05) id 18dIgm-0006Pz-00 for lojban-list@lojban.org; Mon, 27 Jan 2003 15:29:16 -0800 Received: from thedave.homelinux.org (IDENT:1001@localhost [127.0.0.1]) by dave (8.12.4/8.12.4) with ESMTP id h0RNTtiZ008686 for ; Mon, 27 Jan 2003 23:29:56 GMT Received: from localhost (martin@localhost) by thedave.homelinux.org (8.12.4/8.12.4/Submit) with ESMTP id h0RNTsMH008683 for ; Mon, 27 Jan 2003 23:29:54 GMT X-Authentication-Warning: thedave.homelinux.org: martin owned process doing -bs Date: Mon, 27 Jan 2003 23:29:53 +0000 (GMT) X-X-Sender: martin@dave To: lojban-list@lojban.org Subject: [lojban] Re: loi preti be fi lo nincli zo'u tu'e In-Reply-To: <20030124230538.GV7230@digitalkingdom.org> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-archive-position: 3924 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: mbays@freeshell.org Precedence: bulk X-list: lojban-list X-eGroups-From: Martin Bays From: Martin Bays Reply-To: mbays@freeshell.org X-Yahoo-Group-Post: member; u=116389790 X-Yahoo-Profile: lojban_out X-Yahoo-Message-Num: 18389 Sorry I'm so late to reply - I haven't been getting list emails since saturday, just happened to amble onto the Yahoo version. I don't remember offending anyone enough to motivate them to chuck me off the list... did I? 'Scuse weird formatting - copy&pasted from Yahoo General comment: Math World defines set difference in exactly the way that I first did, i.e. A\B == A {intersect} !B. Sort of. See [26]http://mathworld.wolfram.com/ComplementSet.html Yes, but it only really works if you've got a universal set to take the complement in. Admittedly, any superset of A U B will work, but it still seems a bit dodgy if we don't define one. Then again, I don't think it's any less dodgy than the frequent use of {ro da} with a poi clause (like the one in my definition below), so maybe it's not worth worrying about. > [lujvo for set operations]... > How about kaxselcmi and vlinyselcmi? Ooh, I like those. > Just an idea. I'm not sure I like using cec, by the way - to me it > suggests finite sets, when we need a more general term. OK, I can see your point there. > Actually, I've just discovered that jo'e, ku'a and pi'u have rafsi (jom, > kuz and piv) - though I'm not sure what to stick them to. I guess selcmi > would have to do. That still leaves us without set difference, but vlinyselcmi will do. Sorry? vlinyselcmi was meant to be union. Actually, wouldn't plain vicmu do for set difference? > Now we need 2 or 3 versions of the operations - one for the > union/intersection of two sets, one for countably many, and one over > an arbitrary set. Heh. We do? 8) Oh, you're talking about little-upside-down-U versus big-upside-down-U which acts like big Sigma. Kind of, except the big Sigma always has an explicit range over variables (for i from 1 to n, or for i in I), whereas plain Big Intersection followed by a set means... well, what I tried to lojbanise below. > NN gives lujvo for the first two (selcmipi'i and sosyselcmipi'i). We > might just want to have the second, since the first is a special case. > The third, continuing the pattern, would I guess be sorselcmipi'i, > with place structure "x1 is the intersection over x2" - i.e. > > go ca'e ko'a sorselcmipi'i ko'e > gi ro da zo'u > go da cmima ko'a gi da cmima ro de poi cmima ko'e IFF I define X as the intersection over the set of sets? Y, then for all x, IFF x is a member of X then x is a member of all y which are members of Y. Yep. Perhaps that "da cmima ro de" should be "da dunli de" (x is equal to one of the sets in Y)? Nope. That would mean something is in ko'a iff it's in ko'e - i.e. ko'a == ko'e (by extensionality). Maybe a simple example would help - A (intersection) B == (Big intersection) {A,B} Something is in A (intersection) B iff it's in A and it's in B - i.e. iff it's in everything which is in {A,B}. > ...I think. Sim. for union. With that it *should* be possible to do > all the basic set theory you want, though maybe not always elegantly. Works for me so far. 8) > Any idea, for example, how best to translate ('scuse amateur ASCII > graphics): > > | | > | | A > \_/ i > i in I > > ("The union over I of A sub i"), which is the same as > > | | > | | {A : i in I} > \_/ i > > where that big union is my sorselcmipi'i (or sorkuzselcmi)? Do we need > yet another lujvo, or is there a nice translation of that set? I don't > think {lu'i .abu boi xi .ibu poi .ibu cmima tau .ibu} really works. The set of A_i where i is a member of I. Looks fine to me. Really? Cool. I'm still not sure I like it, though, if only because I'm not completely sure how quantification with letterals (and other non-DA pro-sumti) really works. And also what poi-clauses without a ke'a mean. Are they really just the equivalent of the English "such that", or the mathematical "s.t."/":"/"|"? Don't suppose you could point me towards something which explains it all? > Clues, anyone? I think "sorkuzselcmi .abu boi xi da poi ro cmima tau .ibu" works a bit better. Except it doesn't, because apparently you can't have xi da, which is disturbing. 8P I know, which is one reason why I wish I understood letteral quantification. Also - your poi clause isn't a bridi, and I can't work out for sure what it was meant to be. {ro da cmima...}? Does that work? > > > > > > I would like to translate something mathematical and > > > > > > substantial; got any contacts that would like to let us > > > > > > release a translated paper? > > > > > > > > > > Ummm... I guess I could ask someone. Can you be more specific? > > > > > Do you just want some random high-powered maths research? > > > > > > > > What I'd *really* like to do would be a textbook (or, more > > > > likely, a portion thereof), precisely for reasons of > > > > comprehensibility. > > > > > > > > > > That's actually a very good idea. What kind of subject do you > > > want? I (very very vaguely) know the author of a nice+simple > > > complex analysis book, which should be suited to mex. Or else name > > > a subject and I'll see what I can do. > > > > Complex analysis would be cool. I'd also enjoy cryptography, set > > theory, or subatomic physics. Game theory would be hella cool. > > > > Hmmm... > > > > My old Cryptography professor might actually be willing to let me do > > his book. I was supremely fortunate to have > > [28]http://www.cacr.math.uwaterloo.ca/~ajmeneze/ as my crypto prof. > > > > Unfortunately, Handbook of Applied is already freely available, > > which defeats part of my idea (translate something that people > > wouldn't be able to easily get in English, at least without paying, > > and might actually want). > > > > I'm afraid I don't have any tutors/lecturers who've written anything > especially cool... but if the crypto thing doesn't work out give me a > shout and I'll see if I can do 'owt. 'owt? Sorry, couldn't resist continuing the inadvertant rhyming. (It's the opposite of "nowt", if that was a ki'a) (except maybe it should just be "owt"). Well, if you don't mind giving a shot at the complex analysis thing, I'd appreciate it. Then I will. I'll mail my crypto prof about his Elliptic Curves book, if anyone's interested in reading a book on elliptic curve cyphers. 8) In lojban? Of course! BTW, I'm nearly done with [29]http://www.digitalkingdom.org/~rlpowell/hobbies/lojban/algebra.txt Pretty impressive. Which I guess is a compliment to Nick's translation skills, your translation skills, and the ability of Lojban to represent maths. Huzzah all round! --- #^t'm::>#shs>:#,_$1+9j9"^>h>" < v :>8*0\j" o'u" v" e'i" v".neta"^q> ;z,[; > > ^