Definition(Ordered Pairs (Kazimierz Kuratowski;1921)) (a,b){a},{a,b}} Theorem (a,b)=(c,d)→a=c∧b=d Proof. {a,{a,b}={c,{c,d} CASE I:a=b CASE II:a≠b 4口·￥①，43，t夏，里Q0 Jun Ma (majunainju.edu.cn) 1-9 Set Theory (II):Relations 2021年12月02日5/52. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Ordered Pairs (Kazimierz Kuratowski; 1921)) (a, b) , { {a}, {a, b} } Theorem (a, b) = (c, d) ⇐⇒ a = c ∧ b = d Proof. { {a}, {a, b} } = { {c}, {c, d} } Case I : a = b Case II : a ̸= b Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 5 / 52