A touch of MEX

[cbmvax!uunet!mullian.ee.mu.oz.au!nsn]

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 <<lu loi jicmu sidbo pe le
nadmau cmacrnalgebra li'u>> pefi'e la'o <<gy. A. Adrain Albert. gy.>> 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 <<lu
cmacrnalgebra ciste li'u>>
.i ro ciste cu se pagbu loi selci kujo'u su'o se sumti be ri be'o kujo'u loi
selru'a {befi lei selkai {belei selci be'o} pelei se sumti be'o} neme'e <<lu
fintyxu'a selru'a li'u>>
.i vecu'u ledei ckupa'upa'u cu cninyja'o so'o friseljmi sidbo peloi selcmi
ge'uku poi jicmu lei satci se xusra co finti be so'o cmacrnalgebra ciste be'o
poi se skicu 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 ce by. ce cy. zi'epoi cmima lo'iro dacti
	 gi ce'afy. ga'e by. selcmi gi'enaidu .abu
.iseni'ibo go
		ge by. pagbu .abu gi zo'e ji'u cusku me'o by. na'u klesi .abu
	   gi ro cmima be by. cu cmima .abu
.i go meli by. na'u klesi .abu gi by. klesi .abu
.idu'ibo ge zo'e ji'u me'o .abu na'u selkle by. gi .abu selpa'u by.
.i go
	ge meli .abu na'u klesi by. gi su'o cmima be .abu na cmima by.
   gi 	ge by. nalrolmei klesi .abu
	gi zo'e ji'u cusku me'o .abu na'u nalrolmemkle by.
		lo'o.eme'o by. na'u se nalrolmemkle .abu
.i le selcmi be noda cu se cmene <<lu le kunti selcmi li'u>>

(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 ro cmima be
.abu .e by
.i le go'i cu se sinxa me'o .abu na'u selcmipi'i by
.i go meli cy. na'u klesi .abu lo'o.eli cy. na'u klesi by.
   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 .abu by.
.i lego'i cu se cmima ro cmima be .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 je selcmisumji cu frili ke to'erte'i srana za'ure selcmi
.i go .abuxi1 celi'o .abuxiny. selcmi
   gi le sosyselcmipi'i be ro ri be'o no'u li .abuxi1 na'u selcmipi'i .abuxi2
.abuxi3li'o .abuxiny. cuca'e selcmi roda poi cmima role selcmi no'u .abuxi1
celi'o .abuxiny.
.i le sosyselcmisumji no'u li .abuxi1 na'u selcmisumji .abuxi2 .abuxi3li'o
.abuxiny. cu selcmi roda poi cmima su'ole selcmi no'u .abuxi1 celi'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)
	.abuxi1 na'u selcmipi'i .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 ro cmima be .abuxi1 .e .abuxi2 .e .abuxi3
.isi'a meli (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)
	.abuxi1 na'u selcmipi'i .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!*