数学专业英语 ppt课件

and we write A≠B.
集合相等的定义 如果两个集合A和B确切包含同样的元素,则 称二者相等，此时记为A=B。如果一个集合包含了另一个集 合以外的元素，则称二者不等，记为A≠B。
EXAMPLE 1. According to this definition, the two sets {2,4,6,8} and {2,8,6,4} are equal since they both consist of the four integers 2,4,6 and 8. Thus, when we use the roster notation to describe a set, the order in which the elements appear is irrelevant.
The first basic concept that relates one set to another is equality of sets:
只有当省略的内容清楚时才能使用圆点。在大括号中列出集 合元素的方法有时被归结为枚举法。
联系一个集合与另一个集合的第一个基本概念是集合相等。
DEFINITION OF SET EQUALITY Two sets A and B are said to be equal (or identical) if they consist of exactly the same elements, in which case we write A=B. If one of the sets contains an element not in the other, we say the sets unequal
2.3 集合论的基本概念 Basic Concepts of the Theory of Sets
New Words &Fra bibliotekExpressions:
brace 大括号
roster 名册
consequence 结论，推论 roster notation 枚举法
designate 标记，指定
rule out 排除，否决
根据这个定义，两个集合{2,4,6,8}和{2,8,6,4}是相等的，因为 他们都包含了四个整数2,4,6,8。因此，当我们用枚举法来描 述集合的时候，元素出现的次序是无关紧要的。
visualize 可视化
irrelevant 无关紧要的
void set(empty set) 空集
3－A Notations for denoting sets
The concept of a set has been utilized so extensively throughout modern mathematics that an understanding of it is necessary for all college students. Sets are a means by which mathematicians talk of collections of things in an abstract way.
diagram 图形，图解
subset 子集
distinct 互不相同的
the underlying set 基础集
distinguish 区别，辨别 universal set 全集
divisible 可被除尽的
validity 有效性
dummy 哑的，哑变量
visual 可视的
even integer 偶数
When convenient, we shall designate sets by displaying the elements in braces; for example, the set of positive even integers less than 10 is displayed as {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.”
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We use the special notation x S to mean that “x is an element of S” or “x belongs to S”. If x does not belong to S, we write x S .
我们用专用记号来表示x是S的元素或者x属于S。如果x不属于
S，我们记为。
如果方便，我们可以用在大括号中列出元素的方式来表示集 合。例如，小于10的正偶数的集合表示为{2,4,6,8}，而所有正 偶数的集合表示为{2,4,6,…}, 三个圆点表示 “等等”。
The dots are used only when the meaning of “and so on” is clear. The method of listing the members of a set within braces is sometimes referred to as the roster notation.
Sets usually are denoted by capital letters; elements are designated by lower-case letters.
集合论的概念已经被广泛使用，遍及现代数学，因此对大学 生来说，理解它的概念是必要的。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。 集合通常用大写字母表示，元素用小写字母表示。