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We deal with different objects in math such as numbers, functions(函数), operators(算子), and so on. It is important to indicate what kinds of objects we are dealing with before starting our study. Therefore, set plays a fundamental role in math. With different sets, we might have very different results for the same problem. For example, a quadratic equation(二次方程) ax^2+bx+c=0 with a \neq 0 and b^2-4ac<0 has no root(根) in \mathbb{R}(实数) , but two different roots in \mathbb{C}(虚数).

Here we only discuss naive set theory, which is presumed and used in most branches of mathematics. There is a much more strict set theory, which involves a lot of mathematical logic. Because of the reason we mentioned above, it has become the foundation of every other part of mathematics.

Set is one of basis conceptions(概念), which other definitions (定义) depend on. There is no strict (mathematical) way to define what is called a set. It is as if we have to define 1+1=2 and some other laws to define addition(加法). One could also choose to define 1+2=3 firstly, but anyway, there needs to be a initial conception.  Roughly speaking (大概地说), a set is a collection of objects (一些目标对象在一起的整体/汇合) we are interested in, which has specific properties.

1. Terminology and Notation 术语和记号

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