2.3集合的基本概念.pptVIP

§2.3 集合论的基本概念 （Basic Concepts of the Theory of Sets） 课文3－B Subsets(子集) 数词的一些用法 * * 课文3－A Notations for denoting sets 一、生词与词组 set n. 集，集合 subset n.?子集 notation n.记号 roster n.名册 denote v.表示，记 designate v.标记 braces n.(复数)大括号 even integer=even number 偶数 positive number 正数 the underlying set n.基础集，底集 universal set 全集 void set=empty set 空集 dummy adj.哑的；n.哑标 rule out 排除，否决 diagram n.图形，图解 Venn diagrams 文氏图 be divisible by 4 可被4整除的 proper subset 真子集 be said to be 被称为(在下定义时用) the reference to …的注解 be referred to as 被称为 be contained in 被包含在… take the place of 代替 二、要求掌握的句子 1、The concept of a set has been utilized so extensively throughout modern mathematics that an understanding of it is necessary for all college students. 译文：在整个现代数学中集合的概念应用地如此广泛以至于对于所有的大学生来说有必要理解它。 注：这是一个so…that..句型，表示“如此…以至于…”。the concept of 表示“…的概念”。 2、Sets are a means by which mathematicians talk of collections of things in an abstract way. 译文：集合是数学家们用抽象的方式来表述一些事物的集体的工具. 3、Sets usually are denoted by capital letters: A, B, C, …,X, Y, Z; elements are designated by lower-case letters: a, b, c,…, x, y, z. 译文：常常用大写字母A, B, C, …,X, Y, Z来表示集合；而用小写字母a, b, c,…, x, y, z来表示(集合中的)元素。 注：be denoted by…和be designated by…都表示“用…来表示”。 4、We use the special notation x∈S to mean that “x is an element of S” or “x belongs to S”. 译文：我们用专门的记号x∈S来表示“x是S中的一个元素”或者“x属于S”。 5、If x does not belong to S, we write . 译文：若x不属于S, 我们记 。 6、When convenient, we shall designate sets by displaying the elements in braces; for example, the set of positive even integers less than 10 is denoted by the symbol {2, 4, 6, 8} whereas the set of all positive even integers is displayed as {2, 4, 6,…}, the three dots taking the place of “and so on”. 译文：当方便时，我们应当用大括号中的元素来表示集合；例