From lojban-out@lojban.org Sat Jan 25 12:31:26 2003 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_2_3_0); 25 Jan 2003 20:31:26 -0000 Received: (qmail 46809 invoked from network); 25 Jan 2003 20:31:25 -0000 Received: from unknown (66.218.66.216) by m3.grp.scd.yahoo.com with QMQP; 25 Jan 2003 20:31:25 -0000 Received: from unknown (HELO digitalkingdom.org) (204.152.186.175) by mta1.grp.scd.yahoo.com with SMTP; 25 Jan 2003 20:31:25 -0000 Received: from lojban-out by digitalkingdom.org with local (Exim 4.05) id 18cWxZ-0002Gt-00 for lojban@yahoogroups.com; Sat, 25 Jan 2003 12:31:25 -0800 Received: from digitalkingdom.org ([204.152.186.175] helo=chain) by digitalkingdom.org with esmtp (Exim 4.05) id 18cWxP-0002GO-00; Sat, 25 Jan 2003 12:31:15 -0800 Received: with ECARTIS (v1.0.0; list lojban-list); Sat, 25 Jan 2003 12:31:14 -0800 (PST) Received: from rlpowell by digitalkingdom.org with local (Exim 4.05) id 18cWxG-0002GB-00 for lojban-list@lojban.org; Sat, 25 Jan 2003 12:31:06 -0800 Date: Sat, 25 Jan 2003 12:31:06 -0800 To: lojban-list@lojban.org Subject: [lojban] Re: loi preti be fi lo nincli zo'u tu'e Message-ID: <20030125203106.GA7230@digitalkingdom.org> Mail-Followup-To: lojban-list@lojban.org References: <20030124230538.GV7230@digitalkingdom.org> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.5.3i X-archive-position: 3910 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: rlpowell@digitalkingdom.org Precedence: bulk X-list: lojban-list X-eGroups-From: Robin Lee Powell From: Robin Lee Powell Reply-To: rlpowell@digitalkingdom.org X-Yahoo-Group-Post: member; u=116389790 X-Yahoo-Profile: lojban_out 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 http://mathworld.wolfram.com/ComplementSet.html On Sat, Jan 25, 2003 at 05:21:54AM +0000, Martin Bays wrote: > On Fri, 24 Jan 2003, Robin Lee Powell wrote: > > > > > And then if necessary, mexify them with na'u. Have you seen this > > > translation by Nick Nicholas of the start of an abstract algebra > > > book - > > > http://www.lojban.org/files/texts/algebra > > > - which goes some way towards doing that? > > > > I haven't yet read it. .u'uro'a > > > > I'll do that now. > > > > Hmmm. Nick seems to be using selcmipi'i for intersect, which is, > > umm, insane, IMO. I prefer cec to selcmi, but even ignoring that, > > pi'i doesn't even slightly match my concept if intersection; > > cecysi'umi'u is my first try. > > I have a feeling x fa'u + are sometimes used for intersection fa'u > union when considering them as abstract algebraic operations - but I > agree it's not intuitive. Anyway, I'd say selcmipi'i should be the > Cartesian product. I agree. > 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. > 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. > 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. Perhaps that "da cmima ro de" should be "da dunli de" (x is equal to one of the sets in Y)? > ...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. > 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 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 > > 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? Well, if you don't mind giving a shot at the complex analysis thing, I'd appreciate it. I'll mail my crypto prof about his Elliptic Curves book, if anyone's interested in reading a book on elliptic curve cyphers. 8) BTW, I'm nearly done with http://www.digitalkingdom.org/~rlpowell/hobbies/lojban/algebra.txt -Robin -- http://www.digitalkingdom.org/~rlpowell/ *** I'm a *male* Robin. .i le pamoi velru'e zo'u crepu le plibu taxfu .i le remoi velru'e zo'u mo .i le cimoi velru'e zo'u ba'e prali .uisai http://www.lojban.org/ *** to sa'a cu'u lei pibyta'u cridrnoma toi