From @uga.cc.uga.edu:LOJBAN@CUVMB.BITNET Thu Dec 17 08:21:03 1992 Received: from uga.cc.uga.edu by MINERVA.CIS.YALE.EDU via SMTP; Wed, 16 Dec 1992 09:15:06 -0500 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 1088; Wed, 16 Dec 92 05:21:59 EST Received: from UGA.BITNET by UGA.CC.UGA.EDU (Mailer R2.08 PTF008) with BSMTP id 1860; Wed, 16 Dec 92 05:21:53 EST Date: Wed, 16 Dec 1992 21:21:03 +1100 Reply-To: nsn@MULLIAN.EE.MU.OZ.AU Sender: Lojban list From: nsn@MULLIAN.EE.MU.OZ.AU Subject: TEXT.ADV.REV: A Touch Of MEX X-To: lojban@cuvmb.cc.columbia.edu To: Erik Rauch Status: O X-Status: Message-ID: The following is a translation of the first page of _Fundamental Concepts Of Higher Algebra_ by A. Adrian Albert. di'e se fanva fi le pamoi bele'i papri be la'e <> pefi'e la'o <> itu'e CHAPTER I: GROUPS 1. _Sets and mappings._ Abstract algebra is concerned with the study of certain mathematical objects called _algebraic systems_. Each system consists of a set of elements, one or more operations on these elements, and a number of assumptions (about the properties of the elements with respect to the operations) called the _defining postulates_. In this first section we shall introduce some of the elementary notions about sets which form the basis of the precise definitions which we shall present of several algebraic systems. ni'oni'oni'o 1mai cmaci girzu ni'oni'o 1pi'e1mai selcmi ce fancu ni'o le sucta cmacrnalgebra cu srana lenu tadni loi cmaci sibda'i peme'e <> .i ro ciste cu se pagbu lo'isu'ono selci kujo'u su'o se sumti be ri be'o kujo'u loi selru'a {befi lei selkai {belei selci be'o} peva'o lei se sumti be'o} neme'e <> .i vecu'u ledei ckupaupau cu cninyja'o so'o friseljmi sidbo {peloi selcmi ge'uku} poi jicmu lei satci ve satcyskicu {be so'o cmacrnalgebra ciste be'o} poi se srana da'e Let \it A be a set whose elements a, b, c, ... are any objects whatever, and let \it B be a second set. Then we say that B is contained in A, and write B {subset} A, if every element of B is in A. If B {subset} A, we call B a subset of A. We may also write A {contains} B and say that A contains B. If A {contains} B and at least one element of A is not in B, we say that B is a proper subset of A and write A {propercontains} B (A properly contains B), or B {propersubset} A (B is properly contained in A). The set having no elements is called the empty set. ni'oca'e ge tauce'afy. ga'e .abu (to fy. sinxa la fraktur. toi) selcmi da nemu'u nau.abu jo'u by. jo'u cy. zi'epoi cmima lu'i roda gi ce'afy. ga'e by. selcmi gi'enaidu .abu .iseni'ibo go by. pagbu .abu du'i me'o by. na'u klesi .abu gi ro cmima be by. cu cmima .abu .i go li by. na'u klesi .abu jetnu gi by. klesi .abu .idu'ibo {sedu'i me'o .abu na'u selkle by. lo'o} .abu selpau by. .i go ge li .abu na'u selkle by. jetnu gi su'o cmima be .abu naku cmima by. gi by. nalrolmei klesi .abu du'i me'o .abu na'u se nalrolmemkle by. lo'o.eme'o by. na'u nalrolmemkle .abu .i le selcmi be noda cu se cmene <> (NOTE: relations aren't part of MEX like operators are: {du}, {klesi} (subset), {cmima} (element of) etc. are bridi, not MEX operators. To incorporate such relations into MEX (for example, when quoting an equation with {me'o}), {na'u} must be used to convert the bridi into an operator. In that case, {me'o re na'u du re} is the equation "2 = 2", and {li re na'u du re} have the evaluated value TRUE.) The intersection of two sets A and B is the set of all elements which are in both A and B. We designate this set by A {intersect} B. If C {subset} A and C {subset} B, then C is called a common subset of A and B. Every common subset of A and B is a subset of A {intersect} B. The union of A and B is the logical sum of A and B. It consists of all elements which are either in A or in B. We designate it by A {union} B. ni'o le selcmipi'i be .abu poi selcmi bei by. poi selcmi cu selcmi roda poi cmima .abu .e by .i le go'i cu se sinxa me'o .abu na'u selcmipi'i by .i go li cy. na'u klesi .abu lo'o.eli cy. na'u klesi by. jetnu gi cy. kampu klesi .abu joi by .i ro kampu klesi be .abu joi by. cu klesi li .abu na'u selcmipi'i by. ni'o le selcmisumji be .abu bei by. cu logji sumji .abuboi by. .i lego'i cu se cmima roda poi cmima .abu .a by. gi'e se sinxa me'o .abu na'u selcmisumji by. The concepts of intersection and union may be generalised readily to several sets. Thus if A\1,...,A\n are sets, we define their intersection A\1 {intersect} A\2 {intersect} A\2 {intersect}...{intersect} A\n to be the set of all elements which are simultaneously in every one of the sets A\1,...,A\n. The union A\1 {union} A\2 {union}...{union} A\n consists of all the elements in all the sets A\1,...,A\n. Note the the equation (A\1 {intersect} A\2) {intersect} A\3 = A\1 {intersect} (A\2 {intersect} A\3) = A\1 {intersect} A\2 {intersect} A\3 states that the set consisting of those elements in A\1 {intersect} A\2 which are also in A\3 is the same set as that consisting of those elements of A\1 which are in A\2 {intersect} A\3 and that this set is precisely the set of those elements which are in A\1, in A\2, and in A\3. Similarly, (A\1 {union} A\2) {union} A\3 = A\1 {union} (A\2 {union} A\3) = A\1 {union} A\2 {union} A\3. ni'o lesi'o selcmipi'i jo'u selcmisumji cu frili ke selsucta srana za'ure selcmi .i ro lu'a .abuxi1 .eli'o .abuxiny. lu'u poi selcmi zo'u le sosyselcmipi'i be ro ri be'o no'u li selcmipi'i abuxi1 .abuxi2 .abuxi3li'o .abuxiny. cuca'e selcmi roda poi cmima role selcmi no'u .abuxi1 jo'uli'o .abuxiny. .i le sosyselcmisumji no'u li na'u selcmisumji .abuxi1 .abuxi2 .abuxi3li'o .abuxiny. cu selcmi roda poi cmima su'ole selcmi no'u .abuxi1 jo'uli'o .abuxiny .i ko jundi lenu go'e .i me'o (vei (vei .abuxi1 na'u selcmipi'i .abuxi2 ve'o) na'u selcmipi'i .abuxi3 ve'o) na'udu (vei .abuxi1 na'u selcmipi'i (vei .abuxi2 na'u selcmipi'i .abuxi3 ve'o) ve'o) na'udu na'u selcmipi'i .abuxi1 .abuxi2 .abuxi3 cu xusra lenu le selcmi be ro cmima beli .abuxi1 na'u selcmipi'i .abuxi2 be'o poi cmima .abuxi3 cu du le selcmi be ro cmima be .abuxi1 be'o poi cmima li .abuxi2 na'u selcmipi'i .abuxi3 be'o le selcmi be roda poi cmima .abuxi1 .e .abuxi2 .e .abuxi3 .isi'a jetnu fali (vei (vei .abuxi1 na'u selcmisumji .abuxi2 ve'o) na'u selcmisumji .abuxi3 ve'o) na'udu (vei .abuxi1 na'u selcmisumji (vei .abuxi2 na'u selcmisumji .abuxi3 ve'o) ve'o) na'udu na'u selcmisumji .abuxi1 .abuxi2 .abuxi3 --- 'Dera me xhama t"e larm"e, T Nick Nicholas, EE & CS, Melbourne Uni Dera mbas blerimit | nsn@munagin.ee.mu.oz.au (IRC: nicxjo) Me xhama t"e larm"e! | Milaw ki ellhnika/Esperanto parolata/ Lumtunia nuk ka ngjyra tjera.' | mi ka'e tavla bau la lojban. je'uru'e - Martin Camaj, _Nj"e Shp'i e Vetme_ | *d'oh!*