§1.基本概念集合论是数学的许多分支中的一个,今天要讲的是关于它的一些初步知识。首先自然要问:什么是集合?对于这个概念,我们不准备下定义,因为它已经是一个非常基本的概念了。要知道,并不是每一个数学概念都可以定义的,因为假使甲概念要用乙概念来定义,乙概念用丙概念来定义,……这样下去,假使不许循环的话,总要有一些概念是不能定义的。我们就采取“集合”这个概念作为不定义的概念,而仅仅用一些例子来说明它。 §1. The basic concept of set theory is one of the many branches of mathematics. What we are talking about today is some preliminary knowledge about it. The first thing to ask naturally is: What is a collection? For this concept, we are not going to define it because it is already a very basic concept. We must know that not every mathematical concept can be defined, because if the concept of A is defined by the concept of B, the concept of B is defined by the concept of C, ... as it continues, if no circulation is allowed, there must always be some concepts that cannot be Defined. We take the concept of “collection” as an undefined concept, and use only a few examples to illustrate it.