YOU HAVE TO FIX IT! 4口，1①，43，t夏，30Q0 Hengfeng Wei (fweionjn.edu.cn Set Theory:Axioms and Operations 2019 1126 8/38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theorem (Russell’s Paradox) {x | x /∈ x} is not a set. Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 8 / 38
YOU HAVE TO FIX IT! Theorem (Russell's Paradox) xrg rh is not a set. 4口，1①，43，t夏，30Q0 Hengenng Wei hkweionjn.ed.cn Set Theory:Axioms and Operations 2019 1126 8/38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theorem (Russell’s Paradox) {x | x /∈ x} is not a set. Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 8 / 38
Axiomatic Set Theory (ZFC) Ernst Zermelo (1871-1953) Abraham Fraenkel (1891-1965) 4口，1①，43，t夏，30Q0 Hengfeng Wei (hfweiinju.edu.cn)Set Theory:Axioms and Operations 2019 1126 9/38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Axiomatic Set Theory (ZFC) Ernst Zermelo (1871–1953) Abraham Fraenkel (1891–1965) Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 9 / 38
First-order Language for Sets Cset ={E} Parentheses:(,) Variables:,y,Z,.. Connectives:∧，V,,→，→ Quantifiers:V,3 Equality:= Constants: Functions: Predicates:∈ 4口￥0,43，t里，里Q0 Hengong We Chiweinjnedm.cn Set Theory:Axioms and Operations 2019 11 26 10/38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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. Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 10 / 38
First-order Language for Sets Cset ={E} Parentheses:(,) Variables:,,,. Connectives:∧，V,,→，→ Quantifiers:V,3 Equality:= Constants: Functions: Predicates:∈ 4口￥0,43，t里，里Q0 Hengong We Chiweinjnedm.cn Set Theory:Axioms and Operations 2019 11 26 10/38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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. Hengfeng Wei (hfwei@nju.edu.cn) Set Theory: Axioms and Operations 2019 年 11 月 26 日 10 / 38