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集合是现代数学中最基本的概念之一。集合的含义可以这样描述:凡具有某种特性的对象组成的全体就是集合,组成集合的对象叫做这个集合的元素。我们通常用大写字母 A、B、C……表示集合,用小写字母 a、b、c……表示集合的元素。又用符号 a∈A 表示 a 是集合 A 的元素(读作 a 属于 A),用b(?)A 表示 b 不是 A 的元素(读作 b 不属于 A)。集合中元素的特性是识别一个对象是否为该集合的元素的依据。集合的元素可以是任何对象。太阳系的行星可以组成一个集合,一个学校的所有教师可以组成一个集合,一条直线上所有的点可以组成一个集合,大于3小于10的自然数也可以组成一个集合。集合不限定要包含多少个元素。我们把由无限个元素组成的集合叫做无限集合(如自然数集
Set is one of the most basic concepts in modern mathematics. The meaning of a collection can be described as follows: All objects that have certain characteristics form a collection, and the objects that make up the collection are called elements of this collection. We usually use uppercase letters A, B, C ... to represent the collection, and lowercase letters a, b, c ... to represent the elements of the collection. Also denoted by the symbol a ∈ A is an element of set A (read as a belongs to A), b (?) A that b is not an element of A (read as b does not belong to A). The characteristics of an element in a collection are the basis for identifying whether an object is an element of the collection. The elements of the collection can be any object. Solar system planets can form a collection, all teachers in a school can form a collection, all the points on a straight line can form a collection, more than 3 and less than 10 natural numbers can also form a collection. The collection is not limited to how many elements to include. We call an infinite set of infinite elements (such as a set of natural numbers)