YOU HAVE TO FIX IT! 4口，1①，43，t夏，30Q0 Jun Ms (majunnju.edu.cn)Set Theory:Axioms and Operations 2021年11月25日 8/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theorem (Russell’s Paradox) {x | x /∈ x} is not a set. Jun Ma (majun@nju.edu.cn) Set Theory: Axioms and Operations 2021 年 11 月 25 日 8 / 40
YOU HAVE OF议T Theorem (Russell's Paradox) xxgxh is not a set. 4口，1①，43，t夏，30Q0 Jni jmmjtcdncn Set Theory:Axioms and Operations 2021 11 258/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theorem (Russell’s Paradox) {x | x /∈ x} is not a set. Jun Ma (majun@nju.edu.cn) Set Theory: Axioms and Operations 2021 年 11 月 25 日 8 / 40
Axiomatic Set Theory (ZFC) Ernst Zermelo (1871-1953) Abraham Fraenkel(1891-1965) https://encyclopediaofmath.org/wiki/ZFC 4口·￥①，43，t夏里Q0 Jun Ma (majunginjuedu.cn)Set Theory:Axioms and Operations 2021年11月25日9/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Axiomatic Set Theory (ZFC) Ernst Zermelo (1871–1953) Abraham Fraenkel (1891–1965) https://encyclopediaofmath.org/wiki/ZFC Jun Ma (majun@nju.edu.cn) Set Theory: Axioms and Operations 2021 年 11 月 25 日 9 / 40
First-order Language for Sets Cset ={E} Parentheses:(,) Variables:,,2,. Connectives:∧，V,一，→，→ Quantifiers:V,3 Equality:= Constants: Functions: Predicates:∈ 4口，1①，43，t夏，30Q0 Jun 1E (tacmjmcdncn Set Theory:Axioms and Operations 2021 11 25 10/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First-order Language for Sets LSet = {∈} Parentheses: (,) Variables: x, y, z, · · · Connectives: ∧, ∨, ¬, →, ↔ Quantifiers: ∀, ∃ Equality: = Constants: Functions: Predicates: ∈ Everything we consider in LSet is a set. Jun Ma (majun@nju.edu.cn) Set Theory: Axioms and Operations 2021 年 11 月 25 日 10 / 40
First-order Language for Sets Cset ={E} Parentheses:(, Variables:,,z,.. Connectives:∧，V,-,→，→ Quantifiers:V,3 Equality:= Constants: Functions: Predicates:∈ 4口，1①，43，t夏，30Q0 Jun 1E (tacmjmcdncn Set Theory:Axioms and Operations 2021 11 25 10/40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First-order Language for Sets LSet = {∈} Parentheses: (,) Variables: x, y, z, · · · Connectives: ∧, ∨, ¬, →, ↔ Quantifiers: ∀, ∃ Equality: = Constants: Functions: Predicates: ∈ Everything we consider in LSet is a set. Jun Ma (majun@nju.edu.cn) Set Theory: Axioms and Operations 2021 年 11 月 25 日 10 / 40