学习笔记《Set Theory》

学完集合论，终于知道了集合论和群论的差别，集合论是研究集合和集合之间的各种换算和关系，群论是研究一个物体本身的构成关系（翻转、颠倒等等）

集合论：

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.

The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, such as Russell's paradox, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with or without the axiom of choice, are the best-known.

Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.

一个集合论的课程：
https://www.youtube.com/watch?v=HoWC0GQWGaA

符号

属于：

操作符：

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和逻辑符号之间是有一定关联的：

空集（Emptiness）：

Difference：

Symmetric Difference：

Subsets and Supersets（子集和超集）：

Vacuously true（空虚的真、空真）：

Trivial subsets（平凡子集）：

Proper subset（真子集）：

Complement（补集合）：