Naive Set Theory / 素朴集合論（そぼくしゅうごうろん） / Наивная теория множеств / Teoria ingenua degli insiemi

Recommended & Adopted Learning Resources (Online Courses & Textbooks) with Personal Reviews, Personal Writings and Study Archive on Naive Set Theory

A curated collection of recommended and adopted learning resources (including online courses and textbooks) for Naive Set Theory, accompanied by personal reviews of each resource. Also features personal writings across platforms and a systematic study archive, documenting the complete learning process of Naive Set Theory.

Author

Rong-Kang Zhang

Published

2026-03-19

2 尝试粘贴代码块查看编译显示效果

# 验证外延公理（Axiom of Extensionality）
def are_sets_equal(set1, set2):
    """
    判定两个集合是否满足外延公理
    :param set1: 第一个集合
    :param set2: 第二个集合
    :return: 布尔值，True 表示相等
    """
    # 集合相等的充要条件：互为子集
    return set1.issubset(set2) and set2.issubset(set1)

# 测试案例
set_X = {1, 2, 3}
set_Y = {3, 2, 1}
set_Z = {1, 2, 4}

print(f"X = Y? {are_sets_equal(set_X, set_Y)}")  # True（外延公理成立）
print(f"X = Z? {are_sets_equal(set_X, set_Z)}")  # False
# 计算两个集合的交集
Function SetIntersection(setA, setB):
    Initialize empty set result
    For each element in setA:
        If element is in setB:
            Add element to result
    Return result

# 示例：计算 {1,2,3} ∩ {2,3,4}
A = {1, 2, 3}
B = {2, 3, 4}
print(SetIntersection(A, B))  # 输出 {2, 3}
% 罗素悖论：定义集合 R = {x | x ∉ x}
% 推导矛盾：若 R ∈ R，则 R ∉ R；若 R ∉ R，则 R ∈ R
\[
R = \{ x \mid x \notin x \}
\]

% 空集的定义
\[
\emptyset = \{ x \mid x \neq x \}
\]

% 幂集的定义
\[
\mathcal{P}(A) = \{ X \mid X \subseteq A \}
\]

2.1 Videos

3 My Platform Writings on Naive Set Theory (Zhihu, Rednote, etc.)

3.1 Zhihu

3.2 Rednote

3.3 Mathlog

4 Learning Resources

4.1 Textbooks

  • 《Naive Set Theory》(Paul R. Halmos)：经典入门教材，侧重直观理解，适合自学
  • 《Set Theory: An Introduction to Independence Proofs》(Kenneth Kunen)：进阶教材，含公理体系细节

4.2 Videos

4.2.1 Berkeley MATH 135: Naive Set Theory (Full Series)

推荐理由：伯克利大学MATH135课程合集（53条视频），涵盖数理逻辑导论、集合论基本概念、前五个公理等核心内容，讲师Antonio Montalban，适合系统性学习。

5 My Platform Writings on Naive Set Theory (Zhihu, Rednote & More)

5.1 Zhihu Articles

5.2 Rednote Writings

5.3 Mathlog Posts

5.4 Videos

5.4.1 Berkeley MATH 135: Naive Set Theory (Full Series)

推荐理由：伯克利大学经典集合论课程，含53条视频，覆盖数理逻辑导论、集合论基本概念、前五个公理等核心内容，是朴素集合论入门的核心视频资源。

  • 视频链接：伯克利MATH135集合论合集
  • 涵盖内容：01-数理逻辑导论、02-集合论基本概念、03-集合论前五个公理等（共53条）
  • 适用场景：基础理论学习、公理体系梳理
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