2.3集合论的基本概念
单词、词组
1.1 集set，子集subset，真子集proper subset，全集universal subset，空集void/ empty set，基地集the underlying set
1.2 正数positive number，偶数even integer，图形diagram，文氏图Venn diagram，哑标dummy index，大括号brace
1.3 可以被整除的be divisible by，两两不同的distinct from each other，确定的definite，无关紧要的irrelevant/ineential
1.4 一样的结论the same conclusion，等同的效果equivalent effect，用大括号表示集sets are designated by braces，把这
个图形记作A：this diagram is designated by letter A，区别对象to distinguish between objects，证明定理to prove theorems，把结论可视化to visualize conclusions/consequences
汉译英
2.1由于小于10且能被3整除的正整数组成的集是整数集的子集。
The set consisting of those positive integers le than 10 which are divisible by 3 is a subset of the set of all integers.
2.2如果方便，我们通过在括号中列举元素的办法来表示集。
When convenient，we shall designate sets by displaying the elements in braces.
2.3用符号￠表示集的包含关系，也就是说，式子A ￠B表示A包含于B。
The relation ￠ is referred to as set inclusion；We also say that A ￠ B means that A is contained in B.
2.4命题A￠B并不排除B￠A的可能性。
The statement A￠B does not rule out the poibility that B￠A.
2.5基础集可根据使用场合不同而改变。
The underlying set may vary from one application to another according to using occasions.
2.6为了避免逻辑上的困难，我们必须把元素x与仅含有元素x的集｛x｝区分开来。
To avoid logical difficulties, we must distinguish between the element x and the set ｛x｝ whose only element is x.
2.7图解法有助于将集合之间的关系形象化。
Diagrams often help us visualize relations between sets.
2.8定理的证明仅仅依赖于概念和已知的结论，而不依赖于图形。
The proofs of theorems rely only on the definitions of the concepts and known result，not on the diagrams.
英译汉
1.If A is the set of all the letters of the alphabet，then listing each of elements would be tedious.So we write A={a,b,c,…,z}.如果A是所有字母的集合，那么把每一个其中的字母列举出来将是很冗长乏味的，因此我们写出A=｛a，b，c，…,z｝。
2.In the set A，the last element is z.Many sets do not have last elements .Two important sets are N , the set of natural numbers , and W , the set of whose numbers .To list all the elements in these sets would be impoible because they go on forever .So we use three dots and write N={1,2,3,…},W={0,1,2,3,…}.
在集合A里,最后一个元素是z，许多集合没有最后一个元素，两个重要的集合是N，自然数集合，和W，整数的集合。把这两个集合里所有的元素列举出来是不可能的，因为它们是永远持续下去的，所以我们用三个点来表示，集合N写成N={1,2,3,…}，集合W写成W={0,1,2,3，…}。
3.The whole numbers have many important subsets .A whole number is said to be even if it is divisible by 2；2,6,and 18 are examples of even numbers.A whole number is said to be odd if it is not divisible by 2 ; 1,7,and 13 are examples of odd numbers .The natural numbers greater than 1 are called prime or composite , A number is prime if it is divisible only by 1 and itself , A number is composite if it is divisible by a natural number other than 1 and itself.
整数有许多重要的子集。如果一个整数能被2除开就是偶数；2，6，18就是偶数的例子。一个整数如果不能被2整除就是奇数；1，7，13就是奇数的例子。大于1的自然数叫做素数或者合数，如果一个自然数只能被1和它本身整除，那么这个数就是素数（质数），如果一个自然数除了能被1和它本身整除外，还可以被其他的自然数整除，就叫做合数。
