Q:Vhat is“∈”？ Q:What are“sets"? We don't define them directly. We only describe their properties in an axiomatic way. Hengfeng Wei (hfweinju.edu.cn)Set Theory:Axioms and Operations 2019年11月26日11/38
Q : What is “∈”? Q : What are “sets”? We don’t define them directly. We only describe their properties in an axiomatic way. Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 11 / 38
几何原本 Eudlid's Elements (1)To draw a straight line from any point to any point. (2)To extend a finite straight line continuously in a straight line. (3)To describe a circle with any center and radius. (4)That all right angles are equal to one another. (5)The parallel postulate. Hengfeng Wei (hfweinju.edu.cn)Set Theory:Axioms and Operations 2019年11月26日12/38
(1) To draw a straight line from any point to any point. (2) To extend a finite straight line continuously in a straight line. (3) To describe a circle with any center and radius. (4) That all right angles are equal to one another. (5) The parallel postulate. Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 12 / 38
Definition () x生A≌(x∈A). Definition (C) ACB≌x(x∈A→x∈B) Hengfeng Wei (hfweinju.edu.cn)Set Theory:Axioms and Operations 2019年11月26日13/38
Definition (∈/) x /∈ A ≜ ¬(x ∈ A). Definition (⊆) A ⊆ B ≜ ∀x(x ∈ A =⇒ x ∈ B) Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 13 / 38